Offline Model-Based Optimization: Comprehensive Review
Authors: Minsu Kim
Jiayao Gu
Ye Yuan
Taeyoung Yun
Zixuan Liu
Yoshua Bengio
Can Chen
Venue: Accepted by TMLR ()

Abstract: Offline black-box optimization is a fundamental challenge in science and engineering, where the goal is to optimize black-box functions using only offline datasets. This setting is particularly relevant when querying the objective function is prohibitively expensive or infeasible, with applications spanning protein engineering, material discovery, neural architecture search, and beyond. The main difficulty lies in accurately estimating the objective landscape beyond the available data, where extrapolations are fraught with significant epistemic uncertainty. This uncertainty can lead to objective hacking (reward hacking)—exploiting model inaccuracies in unseen regions—or other spurious optimizations that yield misleadingly high performance estimates outside the offline distribution. Recent advances in model-based optimization (MBO) have harnessed the generalization capabilities of deep neural networks to develop offline-specific surrogate and generative models. Trained with carefully designed strategies, these models are more robust against out-of-distribution issues, facilitating the discovery of improved designs. Despite its growing impact in accelerating scientific discovery, the field lacks a comprehensive review. To bridge this gap, we present the first thorough review of offline MBO. We begin by formalizing the problem for both single-objective and multi-objective settings and by reviewing recent benchmarks and evaluation metrics. We then categorize existing approaches into two key areas: surrogate modeling, which emphasizes accurate function approximation in out-of-distribution regions, and generative modeling, which explores high-dimensional design spaces to identify high-performing designs. Finally, we examine the key challenges and propose promising directions for advancement in this rapidly evolving field including safe control of superintelligent systems.

Published in Transactions on Machine Learning Research (01/2026)
Offline Model-Based Optimization: Comprehensive Review
Minsu Kim
minsu. kim&&vrella. quebber
Mila Quebec Al Institute/KAIS
Jiayao (Claris) Gu
yao. www.guummil.mmlll..cmm
Mila Quebec Al Institute/MoGill University
Ye Yuan
jy.guann3@maill.mmgglll
Mila Quebec Al Institute/MeGul University
Taeyoung Yun
laeyoung (ueyoung.uun@mmiin quebec
Mila Quebec Al InsSit
Zixuan Liu
zudkskau@rr..uushiingggn.. eduu
University of Washington
Yoshua Bengio
quebbcc
Mila Quebec Al VuaiituteUUniversity of Montreal
Can (Sam) Chent
can, wwn.chen wwweeleerrrelaaaccmmcmcmcaacaaae quebee
Mila Quebec AI Unniuttt// of Montreal
Reviewed on OpenReview: https: openreview. net/ pet/forum? id= QcS2Wo1TL3
Abstract
Offline black-boz oplimization fundamental challenge science and engineering, where the goal is to optimize black-box functions using only offline datasets. This setting particularly relevant when querying the objective function is prohibitively expensive infeasible, with applications spanning protein engineering, material discovery, neural architecture search, and beyond. The main difficulty lies in accurately estimating the objective landscape beyond the available data, where extrapolations are fraught with significant epistemic uncertainty. This uncertainty can lead to objective hacking (reward hacking) exploiting model inaccuracies in unseen regions- or other spurious optimizations that yield misleadingly high performance estimates outside the offline distribution. Recent advances in model- based optimization (MBO) have harnessed the generalization capabilities of deep neural networks to develop offline-pecific surrogate and generative models. Trained with carefully designed strategies, these models are more robust against didtr---iittiiutionn issues, facilitating the discovery improved designs. Despite its growing impact in accelorating scientific discovery, the field lacks a comprehensive review. To bridge this gap, we present the first. thorough review of offline MBO. We begin by formalizing the problem for both cingle-objective and malti-objectivv settings and by reviewing recent benchmarks and evaluation metrics. We then categorize existing approaches into two key areas: surrogate modeling, which emphasizes accurate function approximation in out-of-distribution regions, and generative modeling, which explores high-dimensional design spaces to identify high-performing designs. Finally, we examine the key challenges and propose promising directions for advancement this rapidly evolving field including safe control of superintelligent systems. For a curated list of resources, please visit our repository
"Minsu and Claris contributed equally this work. i "Coresponneece: can.chen&mila.quehhe chencan421 &gmaai.coom

---

Published in Transactions on Machine Learning Research (01/2026)
1 Introduction
Offline black-bor optimization is a fundamental challenge in science and engincering, where the objective is to optimize a black-box function using only a fixed dataset (Trabucco et al. 2022). This setting has broad applications, including protein engineering (Sarkisyan et al., 2016 Yang et al. 2019), material discovery (Hamidich, 2018). and neural architecture search (Lu et al. 2023). For instance, in neural architecture search, the goal is to identify
architectures solely from existing architecture- performance pairs, without training any new models which can be expensive. Unlike online black-bor opfimization, which allows direct interaction with the objective function, offline black-box optimization is particularly relevant when querying the function is costly, time-consuming, infeasible (Angermüller et al.
2020
Barrera et al. 2016 Sample et al. 2019
Offline black-box optimization is challenging because it requires accurately estimating the landscape of the black-box function beyond the available offline data (Trabucco et al. 2021). Extrapolating into these unseen
regions suffers from significant epistemic uncertainty, arising from limited data coverage and imperfect model knowledge rather than inherent noise (Der Kiureghian & Ditlevsen 2009 which manifests two problematic
scenarios. On the one hand, it may trigger reward hacking (Skalse al. 2022) (which we refer to as objective hacking in our text), wherein the model exploits inaccuracies within the objective estimation in regions beyond offline data, On the other hand, it can give rise to other forms of spurious optimization especially in guided gencrative modeling where the model overfits spurious corrclations within offline data that yicld misleadingly high-performance sample generation outside oflline distribution (Brookes et al. 2019).
Offiine model-based optimization (MBO) is a paradigm that leverages the generalization capabilities of deep neural networks to develop offlino-ppecific surrogate and generative models for solving offiine black-box optimization problems. This progress has spurred two complementary lines of research. One line focuses on building surrogate models that extrapolate beyond the offline dataset, enabling robust function approximation and reliable gradient-based optimization to improve existing designs (Trabucco et al. 2021 Fu & Levine 2021). The other line explores the use of generative models to navigate high- ligh-dimensional design spaces more effectively, facilitating the discovery of high-performing designs underrepresented in the offline data (Kmar & Levine 2020 Kim et al. 2024b). Importantly, these two lines are not mutually exclusive surrogate and generative models often complement cach other to enhance overall performance (Fannjiang & Listgarten] 2020
Chen et al., (024). The design- centric offline MBO differs from offline RL (Levine al.) 2020 Prudencio et al, 2023), which soeks to learn optimal policy from trajectory data and emphasizes sequential decision-making
and credit assignment in Markov decision processes, whereas offline MBO focuses on single-step design generation from static datasets.
Despite the rapid progress in offline MBO, both newcomers and scasoned rescarchers find it challenging to stay abreast of its evolving methodologies. Furthermore, the diversity of approaches and objectives has led to a fragmented landscape, making it difficult to discern overarching trends. To address these challenges, we present the first comprehensive review on offline MBO, synthesizing recent advances, categorizing key areas, and highlighting emerging directions. This review serves as both an accessible introduction for newcomers and a structured synthesis for experts looking to navigate the evolving frontiers of offline MBO.
In this work, we formalize the problem settings for both offline single- and multi-objective optimization (Section]) 2) We also introduce a generative modeling perspective that frames offline black-box optimization as conditional generation, compare single- and multi-objective settings, and discuss the connections between online and offline black-box optimization. Additionally, we review recent benchmarks and propose a taxonomy that categorizes them into four application areas (Section 3): (1) synthetic function, (2) real-world system, (3) scientific design, and (4) machine learning (ML) model. Evaluation costs tend to increase and our understanding of the underlying mechanisms tends to decrease from categories (1) through (3). We address category (4) separately, given its growing prominence in the ML community. For each category, we detail the associated tasks, including the number of objectives and the oracle evaluators. We also provide an overview of the commonly used evaluation metrics, including usefulness, novelty, and diversity.
Next, we categorize existing approaches into two key research lines-as as we have discussed above: surrogate modeling (Section 4 and generative modeling (Section 5p. Importantly, these approaches are not mutually
2

---

Published in Transactions on Machine Learning Research (01/2026)
exclusive, and surrogate models and generative models are often used together in offiine MBO. We separate their discussion in this review to provide clearer insights into each component, while also exploring in detail how they interact and complement one another. Finally, we conclude our paper (Section 6 by outlining promising future directions in this rapidly evolving field. In particular, we highlight several koy areas for further exploration: (1) robust and realistic benchmarking, (2) uncertainly estimalion of surrogale models, (3) causal graphicol surrogate models, (4) advanced generative modeling, (5) and application LLM alignment
and Al Safety. An outline of our paper organization depicted in Figure !
Single-Objective Optimization (500)
Problem Definition
Multi culti-bbecctive Optimization (MOO)
Synthetic Function
Real-World System
Task
Scientific Design
Machine Learning (ML) Model
Benchmark
Usefulness
Eval Metric
Novelty
Diversity
Continuous
Input Representation
Mixed
Discrete
Auxiliary Loss
Data-Driven Adaptation
Training Strategy
Collaborative Ensembling
Offline Model-Based Optimization
Surrogate Modeling
Generative Model Integration
Neural Network (NN)
Model Type
Kernel-Based Model
Learning Rate
Number Iterations
Sampling Strategy
OPT
Test-Time Training
Variational Autoencoder (VAE)
Generative Adversarial Network (GAN)
Autoregressive Model
Generative Modeling
Diffusion Model
Flow Matching
Energy- Based Model
Control by Generative Flow Network (GFlowNet)
Robust and Realistic Benchmarking
Uncertainty Estimation of Surrogate Model
Future Direction
Causal Graphical Surrogate Model
Advanced Generative Modeling
Application to LLM Alignment and Al Safety
Figure 1: Paper overview.
3

---

Published in Transactions on Machine Learning Research (01/2026)
2 Problem Definition
In offline black-box optimization, the goal is to discover new design, denoted by æ", that maximizes the objective(s) f()). This is achieved using an offline dataset D, which consists of N designs paired with their property labels. In particular, the dataset is given by
D = {( y:)
(1)
where each design vector z; belongs to a design space S R., and cach property label yi E R contains the corresponding m objective values for that design. The function f X - R" maps a design to its m-dimensional objective value vector. Offline MBO applies static optimization problems where the objective f(x) is fixed black-box function without temporal structure, distinguishing it from sequential decision-making problems such system identification followed by optimal control (Sutton & Barto 1998
Optimization In offline sinjle-objective optimization (S00), only one objective is considered (i.c., m = 1), leading to the formulation:
a arg max f(x)..
For instance, the design might represent neural network architecture, with f(x) denoting the network's accuracy on given dataset (Zoph & Le 2017].
A prevalent method for addressing this problem involves training a deep neural network (DNN) surrogate model, fa(-), with parameters & on an offiine dataset using supervised learning. The model parameters are optimized by minimizing the mean squared error between the model's predictions and the true labels:
1 Σ (fo(o..) Vi) vi)
6- = arg min à N
After training, the surrogate (.) is employed as stand-in for the true objective function, and design optimization proceeds via gradient ascent updates:
1++1 + V (2r)
m== for E [0,
1], 1J.
where y is the learning rate and is the total number of iterations. The final design, at, then taken as the candidate solution.
A critical challenge of this method is the accurate estimation of the objective landscape beyond the region covered by the offline data. In these extrapolated regions, the surrogate's posterior predictive variance captures its epistemic uncertainty the component due to limited data and model knowledge rather than inherent noise. Formally, if we place a parameter posterior p(0 D) over model parameters, then the predictive distribution under this posterior is
ply x) p(y x, p(0 D) d0,
whose total variance decomposes into
Varly x, D] = Ep( Var(y x, 0) + (ar Bly x, 0))
aleatoric
epistemic
where the first term quantifies alcatoric uncertainty arising from inherent noise in the data, and the second term quantifies epistemic uncerlainty and diminishes as more data are observed (Der Kiureghian & Ditlevsen 2009 In practice, epistemic uncertainty can be estimated via:
Gaussian Processes: posterior variance gives closed-form decomposition Rasmussen & Williams
2006
4

---

Published in Transactions on Machine Learning Research (01/2026)
Deep Ensembles: variance across multiple network predictions approximates parameter uncertainty
Lak
shminarayanan et al. 2017).
Monte Carlo Dropout: repeated stochastic forward passes approximate the weight posterior Ghahramani 2016
Gal &
Bayesian Neural Networks: variational or sampling- based inference yields predictive distributions with parameter uncertainty.
High epistemic uncertainly in out-of-distribution regions can lead to objective hacking, where the optimizer
exploits surrogate inaccuracies to identify spurious high- high-performing designs. We discuss strategies for building robust surrogates in Section
Multi Objectvv Optimization Offline multi-objecttvve optimization (MOO) extends the framework simultaneously address multiple objectives using the dataset D. In this setting, the goal is find solutions that balance competing objectives effectively. For instance, when designing a neural architecture, one might. seek to achieve both high accuracy and high efficiency (Lu et al. 2023 Formally, the multi-objective optimization problem is defined as:
Find x² E X such that there is no E X with f(x) > f(x").
(4)
where f: : X' Rm is the vector of m objective functions and the symbol indicates Pareto dominance. Specifically, a solution æ is said to Pareto dominate another solution x' (denoted f(x) f(x))) if
Vi m., [xx) 2 fi(x') and 3j E (l...., m} such that [5(x)) > fz(x").
(5)
In simpler terms, x is no worse than xt in every objective and is strictly better in at least one. design is considered Pareto optimal if no other design in Pareto dominates it. The collection of all such Pareto optimal designs forms the Parelo set (PS), and the corresponding set of objective vectors,
(f(x) x E PS):
(6)
is known as the Pareto front (PF). The overarching aim in MOO is to obtain diverse set of solutions that closely approximates the PF, thereby capturing the best possible trade-offs among the objectives. Analogous to the single-objective case, a naive approach involves modeling each of the m objectives with separate surrogate models and combining their predictions through a weighted sum to compute the gradient (Mal et al. 2020). However, this approach fails to account for conflicts among objectives and is also susceptible objective hacking. We discuss approaches for addressing these issues in Section 4
Generative Modeling In addition to the surrogate modeling discussed above, generative modeling is another key ingredient in offline MBO. In fact, offline MBO methods can be viewed through the lens of conditional generation, where the objective is to model the distribution p(æ yo) with ye representing the desired conditions. By applying Bayes' rule, this distribution can be decomposed as
p( y.) p(æ)) p(ye x).
From this perspective, offline MBO methods generally fall into two categories: inverse and forward. Inverse methods directly train conditional generative model for p( y.). For example, MIN (Brookes et al. 2019h employs the generative adversarial network (GAN)-based inverse mapping from to to generate designs that meet the desired specifications. Forward methods, on the other hand, leverage surrogate model for p(ye x) to guide an unconditional generative model p(æ). For instance, ROMA (Yu et al. 2021a computes gradients in the latent space of a variational autoencoder (VAE) to iteratively refine generated approaches such as conscrvative objective models (COMs) (Trabucco et al, 2021) and ICT (Yuan al. 2023) fall into this category, although many of these methods do not explicitly model the generative component p(x).
designs. Similarly, gradient-basse
5

---

Published in Transactions on Machine Learning Research (01/2026)
Since the literature on offiine MBO often integrates surrogate and generative modeling, separate their discussion in this review to provide clearer insights into each component: surrogale modeling is discussed in Section g while generative modeling is covered in Section 5 We discuss generative modeling here only at a
high level to provide a novel conditional-gencraiion view of offline MBO, and revisit it in Section 5 for a detailed exposition of methodological developments.
Comparison between SOO and MOO Both single-objective optimization (SOO) and multi-objective oplimization (MOO) strive to optimize objectives using only an offline dataset, which leads to some inherent similarities. In both settings, surrogate models are built to approximate the objective function(s), and generative models are employed to explore the design space efficiently.
However, significant methodological differences emerge due to their distinct optimization goals. One major distinction lies in the training of surrogate models. In SOO, the surrogate is typically trained to minimize the prediction error for a single objective while incorporating relevant priors, thereby facilitating direct gradient-based optimization. In contrast, MOO must capture the interdependencies among multiple objectives, often by leveraging their relationships to enhance surrogate modeling, This challenge usually necessitates the use of multi-task learning strategics (Chen ct al. 2018 Yu et al. 2020).
Another fundamental difference the sampling strategy. In SOO, the focus is on a single property-sin such as model accuracy in neural architecture design which simplifies conditional generation to either computing the gradient of that property (Chen et al. 2023a) building inverse mapping from the property to the design (Kumar& & Levine, 2020). These approaches, however, are not directly applicable to MOO, where improvements in one objective (e.g,, accuracy) might lead to the deterioration of another (e.g., efficiency). Consequently, MOO relies on Parelo-aware sampling strategies to navigate the trade-offs among conflicting objectives. For example, Paretoflow (Yuan et al. 2025 assigns uniform weight vectors to different objectives to guide flow matching towards the Pareto front.
In summary, while SOO and MOO share foundational principles and both contend with out-of-distribution issues, MOO introduces additional challenges related to balancing competing objectives, thereby requiring specialized modeling and optimization strategies.
Relation with Online Black-Box Optimization, online black-box optimázation involves iteratively querying an expensive ground-truth objective function for new design points and then using these new data points to update surrogate model (Jain et al., 2022. Gruver et al. 2023 Frey et al. 2025 :. In high-cost domains such as drug discovery wwhree each experiment (e-g., clinical trial) can be prohibilively expensive (Angermüller et al., [2020] these queries must be made sparingly under a limited budget. A central challenge in online black-box optimization is balancing the tradc-off between designs with high predicted objective values and exploration querying uncertain regions to improve the model's understanding of the objective landscape. This exploration-explitaaiii dilemma has been widely studied in the context of Bayesian optimization (Frazier) 2018)) where acquisition functions such as the Upper Confidence Bound and Expected Improvement are commonly used to guide query selection. This principle has also been explored in the operations research, notably through Efficient Global Optimization (EGO) (Jones et al. 1998).
Bayesian models, such as Gaussian Processes (GPs) Williams & Rasmussen 1995 Rasmussen & Williams 2006), are commonly used for online black-box optimization because they provide principled uncertainty quantification. However, GPs have cubic complexity in the number of data points, which becomes infcasible for large datasets. As result, deep neural networks equipped with approximate uncertainly estimation techniques (e.g., Monte Carlo dropout ensembles) are often employed, though their uncertainty estimates can be less reliable in practice (Gal & Ghahramani 2016 Lakshminarayanan et al. 2017).
In oflline black-box optimization, there is no ability to query the objective after an initial dataset has been collected- effectively a zero-round version of online black-box optimization. Since no further data can be acquired, offline methods often avoid high-uncortainty regions where the surrogate model might be highly inaccurate or risky. Consequently, offline black-box optimization algorithms often adopt more conservative strategies, prioritizing regions of the design space that are both high reward and well-understodd according
6

---

Published in Transactions on Machine Learning Research (01/2026)
to the existing dataset. One example from online black-box optimization is the use of the Upper Confidence Bound (Frazier) 2018), an acquisition function that promotes exploration by combining predicted reward with uncertainty. By adopting a Lower Confidence Bound (Frazier 2018), another acquisition function that promotes exploitation and favors high-reward but low-uncortainty regions, the same principle can be adapted for offline MBO. This contrast ralustrates the core difference between online and oflline black-box optimization: exploration versus conservatism.
Despite these differing strategies seeking to reduce uncertainty versus offline avoiding it-both paradigms rely accurate and scalable uncertainty quantification. Scalable methods for uncertainty estimation can thus benefit both fields. We highlight two candidate methods: Neural Processes, which circumvent the cubic complexity of GPs (Garnelo et al.) 2018), and GFlowNets, which can offer amortized Bayesian posterior inference over the parameter space to estimate model uncertainty (Bengio et al. 2023
Futhermore online and offline methods can synergize naturally. In the online phase, the goal is to collect a high-quality dalaset by judiciously querying promising and uncertain regions. Once the budget for queries is exhausted and the dataset becomes static, offline black-box optimization can then leverage the collected data for final decision. In this way, online black-box optimization focuses acquiring the most informative dataset, while offine black-box optimization focuses on extracting the best solution from the available data.
3 Benchmark
In this section, we present a systematic overview of benchmarks in offline MBO by first categorizing the available tasks in Section 3.1 and then discussing the evaluation metrics in Section 3.2
3.1 Task
We begin by grouping tasks into four main categories: (1) synthetic function, which leverages closed- form mathematical functions to provide efficient, scalable, and analytically transparent benchmarks (see Section 3.1.1]; (2) real-world system, which addresses practical engineering challenges in domains such as
robotics (see Section 3.1.2 (3) scientific design, encompassing applications in biology, chemistry, and material
science (see Section 3.1.3p ; and (4) machine learning model, which includes problems like neural architecture
design (see Section 3.1.4h. Evaluation costs lend to rise and our underslanding of the underlying mechanisms tends to diminish as we move from category (1) to category (3). We address category (4) separately, reflecting its increasing significance within the ML community.
It important to note that these categories are not mutually exclusive; some benchmarks may belong to more than one category. For example, Ehrlich (Stanton et al.) 2024) can be viewed as a synthetic function task for biological sequence optimization, yet mainly discuss it under scientific design to better reflect its application context. Each subsubsection first discusses the intrinsic advantages and limitations of its task category and then introduces the commonly used tasks within that category. For each task, we report its size (i.e., the offline dataset), space (design space), dimension (design dimension), # Obj (number of objectives), and oracle (evaluation oracle type). This organization offers a balanced view both the theoretical appeal and practical applicability of each task category.
3.1.1 Synthetic Function
Synthetic function tasks use closed-form mathematical functions to generate offline datasets for offine MBO methods. During evaluation, these same functions serve as oracles to benchmark these methods. These functions can, in principle, also be applied in an online context; however, in this discussion they serve as benchmarks in the offline setting, where algorithms are limited to using only the offline dataset.
Advantages (1) Computational efficiency: With closed-form expressions, these functions are quick to compute, allowing for extensive experimentation. (2) Scalability: Their ability to be defined for arbitrary input dimensions and numbers of objectives makes them highly adaptable for evaluating algorithms on large-scale problems. (3) Analytical transparency: The known analytical forms enable exact computation
7

---

Published in Transactions on Machine Learning Research (01/2026)
of the Pareto front along with other key properties like gradients and Hessians, which helps in thoroughly understanding both the problem landscape and the behavior of optimization algorithms.
Limitations (1) Lack of realism: The inherent simplicity and often smooth nature of synthetic functions can fail to capture the complexities of real-world problems, including discontimuous or highly constrained landscapes. For example, in protein sequence design, a single amino acid change can cause a dramatic, discontinuous shift in properties, and the design space itself is highly constrained by biological functionality (Angermüller
et al. 2020 Jain et. al.; 2022). Consequently, performance on synthetic tasks may not. directly translate to practical applications. (2) Limited adaptability for deep learning: Deep neural networks have achieved significant success in arcas such as image (Krizhevsky et al., 2012), language (Brown et al., 2020). and molecule (Jumper et al., 2021), and recent work has extended these models to offline MBO (Chen et al., 2023b Watson et al.) 2023). However, synthetic data generated by mathematical functions often lack the rich, complex patterns found real-world data (e.g., molecular structures), which prevents deep learning methods from fully demonstrating their potential in these benchmarks.
Below, we introduce specific synthetic function tasks for both single-objective and multi-objective optimization, covering most tasks from commonly used benchmarks such as the BayesO benchmark (Kim 2023 Surjanovie
& Bingham 2013), holo-bench (Stanton et al., 2024), pymoo (Blank & Deb, 2020), and Oif-MOO-Bench (Xue et al. 2024h. Due to the nature of synthetic function, the evaluation oracle is analytical, meaning that the mathematical form is known. Furthermore, the offline datasct size can be arbitrarily large (Any); however, researchers typically use defaults such as 50 000 (Chen el al.) 2024h for SOO or 60 000 for MOO (Xue) et al. 2024 Yuan et al., 2025). Similarly, many synthetic functions offer the flexibility to operate over any number of dimensions or objectives, and conventional practice often employs specific values (also indicated in parentheses). Finally, the design space in synthetic functions is generally continuous.
Gingl--Obectting Optimization The SOO benchmarks are designed to assess algorithm performance across various landscapes with many local minima, bowl-shaped, plale-shaped, valley-shaped, sleep ridges fillges/dross, drops, and more, each posing unique challenges to optimization (Surjanovie & Bingham 2013).
Oujei-Oeeective Optimization In addition to SOO lasks, many synthetic functions have been developed for the MOO setting, where algorithms often optimize multiple conflicting objectives simultaneously. We discuss four families of synthetic functions for MOO DTLZ (Deb al.] (2055). Omnitest (Deb & Tiwari 2008), VLMOP (van Veldhuizen & Lamont 1999. and ZDT (Zitzler et al. 2000 -cach characterized by distinct Pareto front properties and varying levels of complexity.
3.1.2 Real-World System
Real-world system tasks encapsulate the inherent complexity of practical engineering design. The underlying mechanisms of these designs are generally well-understood, in contrast to the scientific design tasks discussed in the next subsection. While many of these tasks still utilize analytical functions for construction, unlike the purcly synthetic functions, they are derived from models of real-world systems (Tanabe & Ishibuchi 2020). Allernatively, some tasks employ sinulations [Brockman et al. 2016) or surrogate models (Tanabe & Ishibuchi 2020) as oracles, Overall, compared to the synthetic function category, these tasks incur higher ovaluation costs and provide less transparency into the underlying mochanisms.
Advantages (1) Enhanced realism: These tasks are constructed from real engineering systems, and they incorporate real-world constraints such as physical fcasibility, manufacturability, energy consumption, and cost, thereby faithfully representing practical design challenges. (2) Helerogeneous inpul representation: The design spaces often involve a mix of continuous, categorical, and permutation-based variables, mirroring the multifaceted nature of real-world problems. This variety can more effectively test offline MBO algorithms.
Limitations (1) Reduced analytical transparency: While analytical functions offer closed-form expressions, real-world system tasks often rely on simulations or surrogate models that obscure the underlying mechanisms. (2) High evaluation cost: For some simulation tasks, computational expenses tend be high, which may limit the number of feasible experiments (Brockman et al. 2016 (3) Lêmited adoplability for deep learning:
8

---

Published in Transactions on Machine Learning Research (01/2026)
Although these tasks are more realistic than pure synthetic functions, their design is often quite basic Tanabe & Ishibuchi 2020) and may still lack the rich, intricate patterns necessary for deep learning methods to fully demonstrate their potential, similar to the synthetic function tasks.
Below we introduce real-world system tasks. Due to the wide range of tasks, classifying them by application area proves challenging Therefore, we propose to categorize these tasks based on their oracle type- analyyaaal simulation, and surrogate which we believe better reflects the inherent characteristics of each task.
Analytical For some real-world system tasks, the underlying mechanisms are well understood and can be readily represented by mathematical functions. These functions serve as analytical oracles. For example, the RE2-4-1 task in the RE suite (Tanabe & Ishibuchi (220)) involves minimizing both the structural volume and the joint displacement of four-bar truss. This problem is formulated based on Newtonian physics, allowing the oracle function to be derived analytically. Other analytical tasks from the RE suite such as various truss
designs [Cheng & Li 1999 Coello Coello & Pulido 2005 Qian et al. 2025), reinforced concrete beams (Amir
& Hasegawa 1989), ,, pressure vessels (Kanman & Kramer 1994). hatch covers (Amir & &Hasegawa 1989), coil
compression springs [Lampinen & Zolinka| (2000), welded beams (Ray & Liow| [2002), disc brakes (Ray &
Liew
2002); speed reducers (Rarhang-Mehr & Azarm 2002), gear Lrains (Deb & Srinivasan 2006), conceptual
marine design (Parsons & Scott (2044), and water resource planning (Ray et al.) 2001) fall into this category.
The industrial suite benchmarks (Qian et al. 2025) further enrich this category, which are formulated as constrained optimization problems. For instance, the optimal operation lask targets improvements in chemical processing quality, where the objective is to enhance the alkylating product subject to 14 constraints designed to limit onboard fuel and launcher performance. The process flow sheeting problem and process synthesis problem focus on efficient process design under practical constraints. Both objective functions and constraints are expressed mathematically for these tasks. Besides, some classic combinatorial optimization problems in industrial applications such as the multi-objective traveling salesman problem (Lust & Teghemm 2010), the multi-objective capacitated vehicle routing problem (Zajac & Huber 2021), and the multi-objective knapsack problem (Ishibuchi et al. 2015) have analytical formulations that allow for rapid computation. However, these problems are not typically considered traditional design problems.
Simulation Sometimes, even when the underlying mechanisms of task are well understood, their complexity prevents from expressing the oracle in a closed analytical form. In such cases, numerical simulations are used to obtain the oracle, despite the high computational cost often involved. A typical example is robot morphology design. Robot morphology design tasks focus on optimizing the structural parameters of simulated robots to maximize performance on specific tasks, as excmplified by the Ant and D Killly Morphology lasks (Trabucco el al., 2022]. In the Ant. Morphology task, the objective to optimize 60 continuous parameters encoding limb size, orientation, and location for a quadruped robot from OpenAI Gym (Brockman al.] 2016) that it runs fast possible. In the D'Kitty Morphology task, the goal is to adjust 56 continuous parameters defining the D'Kitty robot from ROBEL (Ahn et al. 2020) to enable pre-trained,
conditooned neural network controller, optimized using Soft. Actor Critic (Haarnoja 2018). , to navigate the robot to a fixed location. Both tasks utilize the MuJoCo simulation (Toodrrov lt al.
et al. providing reliable yet computationally efficient performance estimates.
2012 to run simulations for 100 time steps and average the results over 16 independent trials, thereby
This category also includes tasks for electronics design. These tasks focus on optimizing hardware configurations and accelerator architectures to meet specific performance and efficiency objectives, typically involving selecting parameters for processing elements, memory hierarchies, and dataflow patterns, directly influencing factors such as latency (Kumar et al.) 2022). The simulator oracle is used to evaluate the performance and fcasibility of accelerator designs by providing latency, power, and other metrics. Other simulation tasks include radar waveform design (Hughes) 2007) for signal processing, heat exchanger (Daniels et al., 2018) and car structure design (Kohir et al.) (018)) for engineering optimization, TopTrumps (Volz et al. 2019) problem for game- based optimization, and MarioGAN (Volz et al. 2019 for procedural content generation. These tasks provide valuable and diverse benchmarks for offline MBO.
9

---

Published in Transactions on Machine Learning Research (01/2026)
Surrogate Some real-world system tasks utilize surrogate models to approximate the oracle based on simulation data, thereby reducing the cost, of simulations or actual experiments. For instance, several tasks within the RE suite (Tanabe & Ishibuchi] 2020) including vehicle crashworthiness (Liao et al. 2008), car side impact design :Jain & Deb, 2014), rocket injectors (Vaidyanathan et al. 2003 and car cab design (Deb & Jain 2014) employ surrogate oracles. The surrogale paramelers are determined using the response surface method on data sampled from simulations. As a result, these problems differ from their original counterparts, and
the inherent approximations may introduce bias that could affect the reliability of performance assessments.
3.1.3 Scientific Design
In contrast to the engineering problems discussed earlier, scientific design tasks focus on addressing fundamen- tal scientific questions. In the context of offline MBO, these tasks span domains such as biology, chemistry, and materials science, with the aim of discovering novel designs with desired properties. The offline setting is particularly relevant here, as conducting online experiments for these designs is often prohibitively expensive.
Advantages (1) Realistic challenge: Scientific design tasks emulate real-world discovery processes suchh as protein sequence design, molecular optimization, and material discovery that are sufficiently complex to differentiate between various offline MBO methods. Successful optimization in these domains can significantly accelerate scientific discovery and benefit humankind. (2) Deep learning benchmarking: Scientific design problems, including those in biological (Jumper et al. 2021 and chemical (Kuenneth & Ramprasad] 2023) exhibit rich and meaningful patterns. These characteristics provide robust platform to reveal the potential of deep learning-bast offline MBO methods.
Limitations (1) Inaccurale oracles: Unlike synthetic functions with well-defined analytical forms, sci- entific design tasks often rely on approximate oracles-sun such surrogate models or physics-basel based simula- tions resulting in less convincing evaluations. (2) Limited scalability: The size of offline datasets in these tasks is typically quite small, making it difficult to assess the scalability of some methods. Additionally, the predetermined nature of the problem settings (e.g., fixed search spaces and objective counts) limits flexibility in comprehensively benchmarking offline MBO methods.
Below, present specific scientific design tasks across various domains homains-namely namely biology, chemistry, and materials science. These benchmarks offer diverse and challenging scenarios for offline MBO, reflecting the complexity of scientific problems. Given the inherent nature of scientific design, the design space is typically discrele, and evaluation oracles are implemented via surrogale, simulation, analylical, or lookup table.
Biology The biology category encompasses a diverse set of tasks aimed at optimizing biological sequences to enhance their performance. The primary targets in this category are prolein, DNA, and RNA designs. Together, these tasks provide a rich testbed for evaluating the efficacy and robustness offline MBO methods in the life sciences. Below, we describe each design in detail.
Protein Proteins are sequences composed of 20 standard amino acids, and optimizing these sequences can lead to improved properties with applications in antibody development (Luo et al.) 2022 Chen et al.)
2025) and enzyme engineering (Hua et al., 2024). While many tasks have been proposed for protein design (see, e.g., YE et al. (2025)), here we focus specifically on those that address sequence design within the framework of offline MBO.
(1) Green Fluorescent Protein (GFP): Optimizes a 237-length protein sequence to increase fluorescence, using dataset of 56, 086 variants (Sarkisyan et al. 2016 (2) 5' Untranslated Region (UTR) Designs 50-nucleotide sequence to maximize gene expression, predicting ribosome load based on 280, 000 se- quences (Sample et al.) 2019). (3) Adeno-Associated Virus ( (AAV): Optimizes a 28-amino acid segment of
the VP1 protein using 284, 000 variants, largeting improved viral viability (Ogden el al. 2019). (4) E
Ubiquitination Factor (E4B): Enhances ubiquitination activity by optimizing 100, 000 mutations Starita
ct al. 2013). (5) TEM-1 3-Lactamase (TEM): Aims to improve thermodynamic stability, leveraging 17, 857 sequences (Ren et al.) (022). (6) Aliphatic Améde Hydrolase (AMIE): Focuses on boosting enzyme
activity, using 6, 629 variants (Wrenbeck et. al. 2017). (7) Levoglucosan Kinase (IGGK): Targets enzyme
10

---

Published in Transactions on Machine Learning Research (01/2026)
performance improvements, based on 7, 791 mutants (Klesmith et al 2015
(8) (olyyA)-Binadie Protein
1 (Pabl): Optimizes RNA binding efficiency with over 36, 000 sequences (Melamed et al. 2013 (9)
SUMO E2 Conjugase (UBE2I): Focuses on protein function optimization, based on 2, 000 variants (Weile ct al. 2017). (10) Reger: Modifics sequences to maximize bigram counts, simulating sequence editing
2022). (11) Affinity maburation (Affinity): Mulates antibody to maximize binding affinity with the antigen (Chen et al., 2025). (12) Red Fluorescent Protein (RFP): multi-objective
operations (Slanton et al.
optimization problem balancing stability and solvent-accessible surface area (Stanton et al. 2022).
In general, most protein properties are evaluated using surrogate oracles trained on large supervised datasets due to the high cost. of direct evaluation. For some properties such as binding affinity in (11) and stability in (12) simulation oracles (e.g., Rosetta (Alford et al.) 2017) or FoldX (Schymkowitz et al,, 2005) can be employed, though these simulations often lack sufficient accuracy. Similarly, properties like bigram counts can be computed using analylicul oracles; however, such tasks tend to be relatively trivial.
DNA DNA design involves the optimization of sequences comprising four mucleotides (A, C, G, and T). (1) Transcription Factor Binding 8 (TFB8) Optimizes transcription factor binding activity in an 8-length sequence space (Barrera et al.) 2016). (2) Trunscriplion Factor Binding 10 (TFB10); Extends the optimization to a 10-length sequence space, aiming for higher binding affinity (Barrera et al. 2016). Trabucco al.] (2022) further process the data to ensure training set given to offline MBO methods is restricted to the bottom 50%. Oracle evaluation is performed via lookup table oracle, as the properties of all possible sequences have been pre-measured.
RNA RNA design involves the optimization of sequences comprising four nucleobases (A, U, C, and G)- The RNA-Binding task is a typical example. The objective is to optimize a 14-length RNA sequence to maximize binding activity with a target transcription factor. Kim et al. (2023) adopt three target transcriptions, termed RNNA-BindingA (for L14 RNA1), RNA--inding-B B (for L14 RNA2), and RNA- Binding-C (for L14 RNA3). These properties are evaluated using the ViennaRNA package simulation oracle Lorenz et al. 2011
In addition to the above lasks, Stanton et al. (204g) proposes Ehrlich functions, new class of closed-form test functions for biophysical sequence optimization. These functions are formulated to encapsulate key geometric propertics- as non-additivity, epistasis, and discrete fcasibility constraints- that are characteristic of real-world sequence design problems. Their provable solvability, low evaluation cost, and capacity to mimic realistic biophysical interactions make Ehrlich functions a valuable benchmark in offline MBO and a promising direction for future research.
Chemistry The chemistry category comprises tasks focused on small-molecule design, in contrast to the large-molecule design tasks typical in the biology category. Numerous benchmarks for molll-molecule design exist (Brown et al. 2019 Huang et al. 2021 in this paper, we restrict our discussion to those commonly used in offline MBO. Some typical examples include: (1) ChEMBL: Derived from a large-scale drug property database (Gaulton et al.) 2011). this task aims to maximize molecular activity by optimizing the task-specific assay score (MCHC) value. It employs a training set of 1, 093 molecules and a discrete design space of 31-length sequences over 591 categorical values. This benchmark has been incorporated in Trabucco ct al. 2022), where a random forest surrogate used as the oracle. (2) ZINC: This benchmark provides a multi-objective molecule optimization problem involving a small molecule of roughly 128 tokens. The goal is to improve analytical druglikeness properties such as logP (the logarithm of the octanol petanol-water water partition coofficient, reflecting hydrophobicity) and QED (the quantitative estimate of drug-likeness) (Stanton et al., 2022). (3) Molccule: As described in Zhao et al. (022)), this task tackles a two-objective molecular generation problem, aiming to optimize activities against the biological targets GSK33 and JNK3 in a 32-dimensional continuous latent space. Candidate solutions are decoded into molecular strings using a pre-trained decoder.
Material Science Unlike biological tasks focusing on large molecules such as proteins, and chemical tasks centering on small molocules, the material science category is dodicated to designing and optimizing materials based on complex compositional and structural performance metrics. A typical offine MBO benchmark in this domain is Superconductor. Derived from dataset of 21,263 superconductors with annotated critical
11

---

Published in Transactions on Machine Learning Research (01/2026)
temperatures (Hamidich 2018 it has also been incorporated into design-bench TTabucco et al. 2022 The goal is to maximize the critical temperature by optimizing an 86-dimensional continuous representation of material composition, with random forest surrogate serving as the evaluation oracle.
Some less common tasks include:
Crystal structure prediction, which aims to identify stable crystal configurations for a given chemical composition (Qi et al., 2023). These configurations are represented through features such as lattice parameters and Tractional coordinates, and simulalion serves the oracle estimate formation energies.
Battery materials design, where research efforts focus on discovering better active materials for lithium-ion batteries (Valladares et al. 2021
3.1.4 Machine Learning Model
We have discussed three groups of tasks: synthetic function, real-world system, and scientifie design. Tn addition, a widely adopted task in the ML community is the design of machine learning models. This process typically involves optimizing architectures, model parameters, and hyperparameters. The evaluation is generally based on the final performance metrics obtained a test set.
Advantages (1) Practical relevonce: Enhancements in model architectures, parameters, or hyperparameters can yield significant performance improvements, with applications across deep learning, reinforcement learning, and more. (2) Rich offline dolasels: In contrast to scientific design tasks, machine learning models often have access to extensive pre-collected datasets, enabling more robust benchmarking.
(3) Oracle evaluation: In ML tasks, oracle evaluation is performed either via lookup table, surrogate, or through real experiment, offering more accurate assessments compared to the approximate evaluations typical in scientific tasks.
Limitations (1) Limited search space: Although many neural architecture benchmarks provide lookup tables, the available search spaces often constrained and overly simplistic. Tn contrast, real-world architectures tend to be much larger and more complex, leading to higher evaluation costs. (2) Oracle variability; The inherent stochasticity in training deep learning models can introduce significant noise in
performance metrics, which may obscure true improvements and complicate benchmarking.
We categorize these tasks into three major subcategories model architecture, model parameter, and model leperparameeer which are described in detail below.
Model Architecture Model archilecture design, often referred to as newral archilecture search, seeks to automatically discover high-performing network architectures by exploring vast, discrete search spaces.
Early work Zooph & Le 2017) focuses on single-objective optimization and evaluate the discovered architectures via real experiment. The goal is to identify 32-layer convolutional neural network with residual connections that maximizes test accuracy on CIFAR-10. The search space is defined over architectural hyperparameters such as kernel sizes, selected from f2,3, 5, 6}, and activation functions including ReLU, ELU, leaky ReLU, SELU, and SiL.U, resulting in a 64-dimensional discrete space with 5 categories per dimension.
Multi-objective NAS (MO-NAS) extends the search paradigm by simultaneously optimizing multiple performance metrics of neural architectures (Lu et al. 2023). In many MO-NAS frameworks, architectures are pre-trained and their performances recorded in lookup tables, enabling rapid evaluation. Typical objectives include prediction error, model complexity (e.g., number of parameters), and hardware efficiency metrics (e.g., GPU latency or FLOPs). By jointly optimizing these criteria, MO-NAS aims to identify architectures that achieve an optimal balance among accuracy, computational cost, and hardware efficiency. Representative benchmarks include WAS-Bench-22 201hh220--ee -Tet (Krizhevsky 2009) as well the C-10/MOP and IN- IN-1K/N KKMOP suites (Lu et al. 2023
12

---

Published in Transactions on Machine Learning Research (01/2026)
Model Parameter Model parameters are typically optimized via loss functions and gradient- rradeent-based methods. In the context of offline MBO, these parameters are treated as high-dimensional design variables, with a particular focus on agent policy parameters. This category of tasks centers on fine-tuning the neural network weights to enhance performance.
The Hopper task (Trabucco et al. 2022 aims to design a feed-forward neural network controller for 2D hopping robot in MuJoCo (Todorov et al. 2012) to maximize the expected discounted return. The design space encompasses thousands of continuous weight parameters. Crucially, in the offline setting, the algorithm only has access to a dataset of (policy parameters, return) pairs collected from prior RL experiments, rather than interacting diroctly with the environment. Consequently, the policy optimization becomes a purely data-driven, model-based optimization challenge rather than a traditional learning task.
Extending this idea to multi-objective scenarios, Xue et al. (2024) introduce MO-Swimmer and MO-Hopper, where each environment presents two conflicting objectives. In MO-Swimmer, the trade-off is between forward velocity and energy efficiency, while in MO-Hopper, it is between forward velocity and jumping height. Tn both cases, the full set of neural network policy weights constitutes the search space, with data collected by Xu et al. (2020). The multi-objective policy search thus aims to identify new policies that can simultaneously balance these competing criteria without any additional simulation calls.
Model Hyperparameter Model hyperparameters, such learning rate, weight decay, and batch size, play crucial role in controlling the training process. Numerous benchmarks including HPOBench Eggensperger et al. 2021) | exist for this lask, and popular methods like Bayesian optimization (Frazier) 2018) have been widely applied. The objective is to identify the optimal hyperparameter configuration that maximizes a performance metric, typically modeled as a black-box function. To the best of our knowlodge, few offline MBO methods have been developed for hyperparameter optimization. This may be because hyperparameler configurations typically involve simple scalar values, and data-driven offline MBO approaches often relying on neural networks to capture complex design patterns may not be ideally suited for such tasks.
3.2 Evaluation Metric
In this subsoction, we present the evaluation metrics that underpin benchmarking of offline MBO methods. Although have described oracle evaluations when discussing the tasks, it is important to elaborate the evaluation metrics within this context. The oracle evaluation provides a per-sample usefulness score; however, complete assessment requires evaluating set of samples to measure novelty and diversity. In the following, we discuss the motrics for usefulness, novelty, and diversity. We assume that a batch B of candidates (c.g.. K = 128) is used to evaluate these metrics.
3.2.1 Usefulness
The primary criterion is that the candidate set should contain high-performing solutions. In offline SOO, where only one property is considered, this usefulness criterion is straight.orwwrd. In contrast, in offline MOO, usefulness inherently coupled with diversity, as the quality of the solution set is evaluated based on both its proximity to the Pareto front and its distribution along that front. We discuss these two settings separately.
Single-Ojecctive Optimization For SOO tasks, usefulness is evaluated by considering the normalized ground- truth scores of the candidates. Specifically, we examine both the score at the 100th percentile (i.e., the best design) and the 50th percentile (i.c., the median) as suggested in Trabucco et al. 2022 The normalized
score is computed as:
y Mmin
Vn Vnax Vmmin
where y denotes the oracle evaluation score of a design, and ymnin and Dmax are the minimum and maximum scores in the offline dataset, respectively. Additionally, following Jain et al. 2022), the overall performance of a candidate set B is also quantified by its mean score:
Mean(B)- = (. Di
B
13

---

Published in Transactions on Machine Learning Research (01/2026)
where Yi is the oracle evaluation for 2.. This metric provides aggregate measure of the average quality of the candidate designs.
Multi-Objective Optimization In the MOO setting, usefulness is assessed by evaluating both the proximity of the candidate set B to the true Pareto front and its distribution along that front, a metric that naturally also captures diversity. Two widely used metrics are the hypervolume (HV) (Zitzler & Thicle 1998 and the inverted generational distance (IGD) [Bosmann & Thierens 2003).
The HV metric quantifies the size of the objective space that is dominated by the candidate set B and bounded by reference point r = "r'.r"......"" The reference point is typically chosen to be worse than any observed objective value (i.e., a nadir point). Mathematically, the HV is defined as:
HV(B) vol (UIL yEBi-1
where II r'] represents an m-dimensional hyperrectangle (or box) spanning from the coordinates of y to the reference point r along each objective, and vol(.) denotes the Lebesgue mcasure (i.e., volumo) of the union of these hyperrectangles. In simple terms, a larger hypervolume indicates that the solution set both close to the Pareto front and well-distributed across the objective space.
The IGD metric measures the average distance from points the true Parcto front (denoted as PF) to the nearest solution in the candidate set B:
IGD(B, PF)
Σ
min Dps yll-
PPF
VEB
MarEPF
Since the true Pareto front is generally unknown in real-world tasks, most existing studies primarily roly
HV to evaluate MOO performance (Tanabb & Ishibuchi 2020
Xue et al. 2024 Yuan et al. 2025
3.2.2 Diversity
Diversity quantifies the spread or variability within the set of generated candidate designs, and maintaining higher diversity helps reduce the risk that all candidates fail due to similar underlying limitations (Jain et al. 2022 Kim et al. 2023 Kirjner et al. 2024). In offline MBO, it is crucial not only to identify high-perlorming designs but also to explore diverse regions of the design space, thereby capturing multiple modes of the black- box function. A common metric for measuring diversity is the average pairwise distance between all distinct candidates in the set B, defined as:
Diversity(B) B B 1)
Σ
Σ (m5-8r) (my (
5(x,, x.,);
(BL.B.)B
where ö(r;; æT) denotes a distance measure (e-g., the Fuclidean distance for continuous designs or the Levenshtein edit distance (Haldar & Mukhopadhyay 2011) for discrete designs). Alternatively, the median of the pairwise distances may be used instead of the mean (Kirjner et al. 2024). A higher diversity score indicates that, average, the generated designs more varied within the batch B.
Another related metric is coverage, as adopted in Yao et al. (0225) which evaluates how well the batch of candidate designs collectively spans the search space. It is computed as:
LIC(B) Σ max i
Lih
where the number of design dimensions and Ei denotes the k-th component of the i-th design æ; Note that this formulation assumes continuous representation of the design; discrete designs must first be embedded into a continuous latent space. Intuitively, higher coverage value indicates that the designs in B more widely spread across each dimension, suggesting improved diversity.
14

---

Published in Transactions on Machine Learning Research (01/2026)
3.2.3 Novelty
Novelty measures the degree to which the newly generated candidate set B differs from the offline dataset D, thus promoling exploration beyond known designs.. In oflline MBO, is important that the proposed candidates not only perform well but also explore regions of the design space that are distinct from known designs. Novelty is typically quantified by computing the mcan of the minimum distances between cach candidate in B and the closest design in D (Jain et al. score is defined as:
2022
Kim et al. 2023 Mathematically, the novelty
Novelty(B)
Σ
min 6 ([i at),
B
#ED
where 8(2;, æ) denotes the distance metric between design æ; from B and design from D. As before, the Euclidean distance is commonly used for continuous designs, while the Levenshtein edit distance (Haldar & Mukhopadhyay 2011] is appropriate for discrete designs. Alternatively, one may use the median of the minimum distances instead of the mean (Kirjner et al.) 2024). A higher novelty score indicates that, on average, the generated designs are more dissimilar from those in D, thereby fostering the discovery of innovative and unexplored designs.
Overall Summary Most offline MBO methods (Trabucco al. 2021 Chen et al. 2023a) primarily focus the usefulness metric, it is the fundamental measure of candidate quality. However, diversity and novelly are also important for comprehensive evaluation. We conjecture that this focus is partly due to the relative ease of demonstrating improvements in usefulness, whereas proving enhancements across all three metrics for a proposed method is more challenging. We encourage future research to consider all metrics.
Besides, some recent work has proposed alternative metrics beyond the three discussed above. For instance, Qian et al. (2025) roduces a slabilily metric that measures an algorithm's ability to consistently surpass the performance of the offline dataset during the optimization process. Specifically, this metric evaluates not only the final design but also all intermediate samples along the optimization trajectory, thereby assossing whether these intermediate solutions can outperform the best design in the offline dataset- critical consideration given the challenge of determining an appropriate stopping point in offline MBO.
4 Surrogate Modeling
Offline MBO learns surrogate model that approximates the black-box oracle and leverages it to guide design oplinization. As shown in Eq. (2), the mean squared error loss is employed to fit the surrogate model loss that can also be interpreted as maximum likelihood loss when accounting for uncertainty (Chen et al., 2024). In this work, we decompose surrogate modeling into four key components: input representation, model type, braining stralegy, and sampling siralegy.
4.1 Input Representation
The inpul represenlation refers to the lype of design æ,, which we categorize into continuous, discrele, and mized representations. Since we focus on offline MBO, the ability to compute gradients of æ is a vital property of the surrogate model. For discrete and mixed representations, common strategy is to transform them into a continnous space facilitate gradient computation.
Continuous Continuous representations are the most common and are often used directly in their native space due to their inherent contimuity. For example, in the superconductor task, the search space is an 86-dimensional continuous vector representing the elemental composition of superconductors (Hamidieh) 2018). Other examples include Ant Morphology and D'Kitty Morphology, where the task is to optimize the morphology of quadrupedal robots using 60 and 56 continuous parameters respectively to enhance locomotion, and Hopper Controller, which involves optimizing a neural network policy with 5126 continuous weights maximize return (Brockman et al.) 2016). The continuous nature of these representations naturally facilitates gradient computation. An interesting case image optimization; for instance, DeepDream optimizes continuous images using surrogate gradients enhance specific features (Mordvintsev et. al. 2015
15

---

Published in Transactions on Machine Learning Research (01/2026)
Even when using continuous inputs, it is common to map them into the latent space of a generative model for optimization and manipulation, as this latent space can better capture the semantic meaning of the design. For example, classifier (or surrogate) guidance optimizes the continuous image latent space, steering samples toward a specific category in diffusion DDariwal & Nichol 2021 and flow matching models (Dao et al. 2023
Discrete In many real-world applications, the design æ is discrete. The most common representation is calegorical encoding, which is suitable for unordered discrete variables. Typical applications include neural architecture search, biological sequence design, and molecule design. When computing surogaat gradients on categorically encoded inputs, three strategics are typically employed. First, one may remain in the raw discrete space and use discrete gradient estimators to approximale gradients (Bengio et al. 2013 Jang et al. 2017 Chen et al. 2023b). Second, the input can be mapped into latent space where gradients are more directly accessible (Luo et al. 2018 Gómez-Bombarell et al. 2018). Third, the design may be transformed into a continuous representation through design-specife modeling. For instance, Liu et al. (2019); Fu et al. (0022) propose continuous relaxations of discrete representations for neural architectures and chemical structures,
respectively, to facilitate gradient computation.
A less common discrete representation is permutatiion encoding, which used when the relative order of elements is crucial. This encoding is typical in problems such as the traveling salesman problem (Lust & Teghem 2010). However, these problems generally do not rely on surrogate models since their final solutions can be evaluated elficiently.
Mixed Some optimization problems involve combination of continuous and discrete variables, leading to hybrid inpul represenlations that require domain-specific surrogale modeling. For instance, in protein property prediction, a protein is characterized by both continuous atom coordinates and discrete residue types. A practical surrogate model is to input the discrcte residuc types into a pro-trained language model to obtain residue embeddings, and then feed both the residue embeddings and atom coordinates into a graph neural network for the final prediction (Wang et al.] 2022 Zhang et al. 2023 Chen et al. 2023c). In this scenario, gradient computation leverages strategies developed for both continuous and discrete representations.
4.2 Model Type
Surrogate models can be broadly classified based on their parameterization into parametric and non-porametric models. Parametric models have a fixed number of parameters determined by their architecture, whereas non-parametric models adapt their complexity based on the available data (Hastie et al. 2009]. In the context of oflline MBO, neural networks are the predominant parametric models, whereas kernel-based models are the typical non- -onmmmmmtt choices.
Neural Networks (NN) Neural nelworks are a class of parametric models where the architecture (e.g., the number of layers and neurons per layer) is predetermined prior to training (LeCun et al., 2015). These models approximate the target function by optimizing a fixed set of parameters, making them well-suited for high-dimensional and complex tasks. Owing to their generalization capabilities and scalability, NN-based surrogate models have become increasingly popular in offline MBO (Trabucco et al.
2022
Some approaches use data-agnostic neural networks such as multi-layer perceptrons (MLPs) as surrogate models (Trabucco et al. 2021 Yu et al. 2021a Yuan et al., 2023 Chen et al.
2023a While these
methods demonstrate the overall effectiveness of the optimization framework, simple MLPs may struggle to accurately capture the intricacies of complex black-box functions, especially when the design itself contains rich semantic information. To better exploit domain-specific information, recent works have designed specialized architectures tailored to the data. For example, Lee et al. (2023) employs graph neural network (GNN) designed for modeling molccular propertics and guiding molecule generation, while Chen et al. (2025) uses a protein language model lo extract residue embeddings that feed into a GNN for predieting antibody binding affinity, thereby steering antibody structures towards a more stable conformation. OmniPred (Song et al.) 2024) employs specialized neural setwwor--socfffcalll, a language data comprising both textual and numerical modalities, and estimates prediction uncertainty by analyzing the concentration of sampled outputs.
on hetcrogencous offline
16

---

Published in Transactions on Machine Learning Research (01/2026)
It is regression, polynomial regression, and support vector machines (SVM)- are also useful (Hastie et al. 2009 However, in offline MBO, these alternatives are used less frequently, as the current surge in offine MBO has largely been driven by advances in deep NNs due to their superior generalization ability and scalability.
worth noting that besides neural networks, other parametric models-suee as linear regression, logistic
Kernel-Based Model In offline MBO, the offline datasct is often limited, making non-paramctric kernel- based models particularly attractive. Their effective complexity increases with the mumber of data points. enabling them to capture intricate function behaviors while providing principled uncertainty estimates (Ras- mussen & Williams 2006). Gaussian Processes are the most widely used kernel-based models, offering closed-form posterior inference and calibrated uncertainty (Frazier 2018). Although offinne MBO does not allow further queries of the black-box function, uncertainty quantification remains crucial: it helps identify regions in the design space where the surrogate's prodictions are less reliable. This information can be used to guide conservalive optimization strategies that avoid over-oplimistie predictions in poorly sampled areas.
Chen et al. 2022b demonstrates that the neural tangent kernel associated with infinite-width neural networks can be more effective than standard kernels like the radial basis function (RBF) kernel. Furthermore, Chen el al. (202bb) introduces a kernel parameterized by pre-trained biological language models for biological sequence design. In cases where pre-trained models are unavailable, deep kernel learning can be employed to learn the kernel directly from the data, with scalability achieved via inducing points (Wilson et al., 2016).
Besides kernel-based models, other non-parametric methods- such as k-nearest neighbors (kNN) and random forests- also serve as surrogate models. However, these approaches are typically non-differentiable and do not naturally provide robust uncertainty estimates, which makes them less suitable for gradient-based optimization in offline MBO (Hastie et al. 2009).
4.3 Training Strategy
To enhance generalization and robustness, surrogate models often incorporate specialized training strategies. We categorize these into four groups: auziliory loss, dala-driven adoplation, collaboratice ensembling, and generative model integration. Note that a single method can span multiple categories due to its inherent complexity. In such cases, the method may be discussed in more than one group, with emphasis placed on the aspect most relevant to that group.
Auxiliary Loss Auriliary losses are incorporated into surrogate models to refine the training process by encouraging specific model behaviors, as detailed below.
Conservatism is a widely adopted strategy in offline MBO. Inspired by similar ideas in offline RL YYu et al., 2021b). Trabucco et al. (2021) trains the surrogate to systematically undercstimate the truc objective on out-of-distributioon inputs by identifying polential adversarial examples via gradient ascent and penalizing the surrogate's predictions at these points, thereby enforcing a conservative estimate. In Qi et al. (2022), offline MBO is reframed domain adaptation problem by treating the offline dataset as the source domain and the optimized designs as the target domain. A distributional distance loss is used to ensure that the surrogate produces conservative (i.e., less overconfident) predictions when evaluated on samples far from the offline distribution. Further, [Chen et al. (2022b 2023b) propose a bidirectional learning framework that integrates knowledge from an offline dataset into a high-performing design using both forward and backward loss mappings. Here, a kernel-based model provides a closed-form solution while the backward mapping serves as a regularizer to mitigate the impact of out-of-distribution inputs. While this method technically regularizes the designs rather than the surrogate itself, it still promotes conservatism by encouraging generated designs to remain close to the offline dataset. This principle is closely related to distributionally robust optimization (Delage & Yel 2010), which aims to avoid overconfident decisions under uncertain region.
Smoothness is another important strategy for improving generalization. Yu et al. (2021a) smooths the oflline data with a Gaussian filter, finds the weight perturbation that maximizes the loss, and then adjusts the model parameters to maintain local smoothness with respect to both the inputs and the weights. In the same vein, Dao et al. (2024a b) incorporate measures of model sharpness and sensitivity, respectively, to constrain the surrogate's 's local behavior and improve its stability.
17

---

Published in Transactions on Machine Learning Research (01/2026)
Ranking Consistency is another strategy used in offiiee MBO. In many cases, the surrogate is tasked with selecting promising designs rather than predicting precise objective values. To support this, (Tan et al. (2025 employs a listwise ranking loss that encourages the surrogate to preserve the relative ordering of candidate
designs. In scenarios where pointwise labels are noisy or unreliable- such as with augmented data Chen et al. (2023a) adopts a pairwise ranking loss, remonstrating improved robustness over traditional mean squared error losses. In essence, ranking- based losses provide discrete, relative supervision that enhances the surrogate's robustness and decision-making reliability.
Gradient Alignment is exemplified by Hoang et al. 2024)) which demonstrates that the effectiveness of optimization is strongly correlated with how well the surrogate's 's gradient field aligns with the underlying gradients of the oflline data. To this end, the authors propose a dedicated loss function to enforce such alignment and improve optimization quality.
Finally, auxiliary losses naturally extend to multi-objoctive scttings. Multi-task learning techniques such as GradNorm (Chen et al.] 2018) and PeGrad (Yu et al.) (020) can be used so that learning one property via a surrogate task aids in predicting another-a valuable capability in domains like biology where labeled data is often limited (Xu et al. 2022
Adaptation Data-driven adaptation generally falls into three categories:
Sample Reweighting This method assigns higher weights to samples deemed more relevant. For instance, Yuan et al. (2023) leverages bi-level optimization (Chen et al. 2022a) to learn weights for generated samples, thereby mitigating noise and enhancing surrogate. Similarly, AutoFocus calculates offline sample weights as the ratio of the probability under the search model to the initial probability, effectively refining the surrogate in the most relevant design regions (Fannjiang & List 2020
Synthetic Data Generation Syuthetic data is extensively used in offiine MBO. For example, Trabucco et al. 2021) employs gradient ascent to generate adversarial designs, penalizing the surrogate on these points. Morcover, Chen et al. (2023a) and Yuan et al. (2023) apply pscudo-labeling for nearby points based surrogate predictions, filtering out noisy samples to further improve the surrogate.
Domain Knowledge Injection Incorporating domain-speeific knowledge can enrich the surrogate model's understanding and enhance its extrapolation capabilities. For instance, Chen et al. (0223)) leverages a pre-trained biological language model (raltte on millions of biological sequences a feature extractor, yielding superior performance compared to models without pre-training. Furthermore, Kuba ct al. (024b) introduces Functional Graphical Models that build a data-specific graph capturing functional independence properties, thereby imposing a structural bias that benefits blck-box optimization and mitigates distribution shifts.
These data-driven techniques are applicable not only to surrogate modeling but also to generative modeling, discussed in Section 5 In addition to auriliary losses and data-driven adaptations, training strategies also benefit from insights drawn from peer models and generative models, as described next.
Collaborative Ensembling Ensemble learning techniques combine predictions from multiple models to achieve improved performance and generalization compared to individual base learners (Hansen & Salamon, 1990: Dietterich 2000). In the context of offline MBO, recent studies have focused on developing ensemble- based surrogate models tailored to these settings. For example, Chen et al.] (2023a) and Yuan et al. 2023 employ a mean ensemble of surrogates, wherein multiple models exchange valuable sample information during optimization to enhance learning contrasting with traditional ensembles that generally interact only during aggregation. Additionally, Fu & Levine (2021) introduces innovative approximation of the normalized maximum-likelihood (NML) distribution to construct an uncertainty-awant forward model. For each optimization point, the approach assigns multiple labels and trains separate models on each point-label pair, with the resulting ensemble estimating the conditional NML distribution to provide robust surrogate predictions that guide the design optimization process. Furthermore, Kolli (2023) tackles gradient conflicts among ensemble members by employing multiple gradient descent steps and conflict-averse gradient descent, thereby striking a balance between conservatism and optimality.
18

---

Published in Transactions on Machine Learning Research (01/2026)
Generative Model Integration Surrogate models often guide the sampling process of generative models, and in turn, several studies leverage insights from generative models to further enhance surrogate modeling. For instance, Fannjiang & Listgarten (2020) employs a variational autoencoder to model both the offline data distribution and the search model distribution, using the ratio of these probabilitics as an importance weight to retrain the surrogate. Similarly, et al. (2022) trains a GAN discriminator to different iate between the offline distribution and the desired design distribution, subsequently fine-tuning the surrogate yield mediocre predictions when designs deviate significantly from the offline data. Moreover, Chen al. (2024) derives conditional distribution from diffusion model, which is used to regularize the surrogate by minimizing the KT. divergence between the surrogate's output and the derived distribution.
Practical Guide on Selecting Training Strategies We have discussed various training strategies, which typically complement rather than conflict with each other. Choosing the appropriate strategy depends primarily on the intended use-case and the operational context of the surrogale model. Below, we provide practical guidance for selecting among these strategies:
When using the surrogate model for gradient- based optimization (e.g. gradient ascent), conservatism- based approaches such as conservative objective models (COMs) (Trabucco et al. 2021 are particularly effective. For scenarios where the surrogate's primary role is ranking and selecting promising designs, strategies emphasizing ranking consistency crucial (Tan et al. 2025 Chen et al. 2023a Additionally, if the surrogate exhibits sensitivity to perturbations in inputs weights, smoothness strategies can be
prioritized Yu et al. 2021a
In sinuations where robust generative model available, one may (1) employ sample reweighting, adjusting the sample weights based on the probability ratio between the offline and search distributions, thus refining surrogate training; (2) identify out-of-distribution samples by leveraging GAN discriminator (Qi et al.) 2022) by directly computing likelihood scores (Chen et al. 2024 (3) generate additional synthetic samples with pseudo-labeling to improve the surrogate.
Domain knowledge injection highly effective when pre-trained, domain-specific models are accessible. These can serve as feature extractors improve extrapolation performance (Chen al. 2023b).
Ensemble-basee based predictions generally outperform individual surrogate predictions, making collaborative ensembling effective when computational resources allow (Chen et al.) 2023a Yuan et al. 2023
4.4 Sampling Strategy
Once the surrogate model is trained, gradients are computed to guide the sampling process. The typical procedure is outlined in Equation (3 with the general form given by:
Ft- 2 + n- - O (o) I=a.), for & 1].
(8)
This section discusses key aspects of the sampling process: the learning rate n,, the number of iterations T, the optimizer OPT, and test-time training.
Learning Rate Selecting optimal learning rate 7) poses significant challenge in offline MBO due to the absence of a dedicated validation set. While Beckham et all (2024) suggests the introduction of validation set in offline MBO, this method may require sacrificing some high-performing data. Additionally, Chen let al. (2023b) proposes training an auxiliary model to provide weak supervision signals for optimizing the learning rate, thus enhancing sampling effectiveness. Similarly, CCemiingii et al. (2024) formulates offline MBO as an offline reinforcement learning problem, where learned policy takes the current design as input and outputs the optimal learning rate; however, this approach may still be vulnerable reward hacking due to out-of-distribatiion issues in the surrogate model.
19

---

Published in Transactions on Machine Learning Research (01/2026)
Number of Iterations The number of optimization steps, denoted as T, is another vital hyperparameter. Determining the appropriate T is challenging due to the absence of ground-truth function, which raises concerns about overfitting, This hyperparameter also correlates with the learning rate: a higher learning rate might necessitate a smaller T to avoid deviating from the distribution. The strategy suggested by [Trabucco) et al. 2021 involves using 50 steps to generate adversarial samples and regularizing the surrogate model based on these samples. Subsequently, a similar 50-step approach is employed during the sampling phase. Meanwhile, Yu al. 2021aa; Fu & Levine (2021) report that their methods remain robust even as T increases. Furthermore, Damani et al. (0233 proposes training binary classifier to distinguish offine data from design data, observing that the degree of distribution shift depends on T. The classifier logits serve as a proxy for distribution shift, allowing users to constrain T to regions where the surrogate predictions remain reliable.
The term OPT denotes the optimizer, which be an algorithm such as SGD, Adam, etc. (Ruder These optimizers are typically applied to offline SOO. In offline MOO, however, multiple gradients must be managed simultaneously, A naive approach of computing weighted sum of these gradients often results in conflicts that hamper effective optimization. Recent methods address these conflicts: the multiple gradient descent algorithm (Désidéri 2012) finds a common descent direction by assigning nonnegative weights that minimize the norm of the combined gradient, while PCGrad (Yu et al. 2020 resolves conflicts by projecting one gradient onto the orthogonal space of another when their inner product negative, thereby enhancing robustness in multi-objective settings.
OPT
2016
Test- Training A common sampling strategy involves adapting the surrogate model at the current optimization point. While this concept overlaps with the training strategies discussed in Section [13] the focus here is on fine-tuning the surrogate locally. Given the impracticality of optimizing the surrogate globally, it is more feasible to refine its performance near the current point. For example, Fu & Levine (2021) estimates the conditional normalized maximum likelihood by incorporating the current point into the surrogate modeling procoss, and (Yu ct al.] 2021a) adjusts the surrogate to increase local smoothness. Morcover, Chen et al. (2023a); Yuan et al. (2023) generate pseudo pairwise and pointwise labels in the neighborhood to further refine the surrogate's s local behavior.
5 Generative Modeling
In addition to surrogale modeling described in Section generalive modeling plays a pivotal role in offline MBO. The high-dimensionallty of design spaces renders exploration challenging, and generative models offer an effective means to navigate these spaces. As detailed in Eq. 7 offline black-box optimization can be framed as a conditional generation problem, where the objective is to model the distribution p(æ yo) with ye representing the target conditions. By Bayes' rule, this distribution proportional to the product of the prior p(x) and the likelihood p(y. æ). Broadly, two categories of conditional generation emerge in this context:
Inverse This approach directly trains a conditional generative model learn the mapping from target conditions ye to designs æ, thereby capturing p(= y²) and enabling conditional sampling.
Forward This approach leverages a surrogate model for p(ye x)) to steer an unconditional generative model p(æ) toward desirable designs. A notable special case is the use of direct gradient ascent, which bypasses the need to explicitly model the generative component p(x).
In the remainder of this section, we first outline the general principles of these generative models-including variational auloencoder (VAE) (Kingma & Welling, 2014), generative adversorial network (GAN) GGoddellow lt al.) 2014),, autoregressive model (Vaswani et al.) 2017), diffusioo model (Ho et al. 2020). flow match- ing (Lipman et al.] 2023) and eneryy-based model (EBM) (LoCun et al., 2006)-followee followwd by discussion on
how they achieve conditional generation within offline MBO. Finally, we introduce Generotive Flow Network (GFlowNet) (Bengio et al. 2023), a versatile control strategy applicable to wide range of generative models.
20

---

Published in Transactions on Machine Learning Research (01/2026)
5.1 Variational Autoencoder (VAE)
General Principle Variational Autoencoders (VAEs) integrate ideas from variational inference and au- toencoders to learn probabilistic latent representation for the data (Kingma & Welling 2014). The model expresses the data likelihood as
p(a)= - p())))))(())
and introduces an approximate posterior ( to facilitate efficient inference. In particular, the VAE adopts an encoder-decoder architecture: the encoder approximates the posterior q (g(22ag (z),,,, while the decoder models the likelihood (=)
Conditional Generation In the context of VAEs, conditional generation can be achieved through two categories of methods: inverse and forward methods. The inverse method directly trains a label-conditioned VAE to learn the mapping from target conditions to designs. For example, [Bookkes al. (2019) adaptively trains the VAE on high-performing designs (such as protein sequences), enabling the direct sampling of promising candidates without the need for an external surrogate model.
In contrast, forward methods are more commonly employed, leveraging the continuous latent space of the VAF. Here, an unconditional VAE is first trained to embed designs into a continuous latent space, after which a surrogate model supplies gradient information to steer the latent codes toward regions corresponding to improved designs. This approach is particularly beneficial for discrete design optimization, as demonstratod by works on general discrete designs (Yu al. 2021a) and discrete molecules (Gōmez-Bombbrelll 2018), which map these designs into latent space amenable to gradient-based optimization. Together, these methods illustrate how VAEs can effectively navigate high-dimensional design spaces, either by directly conditioning on target attributes via the inverse method or by leveraging gradient- tradient-driven manipulations within the latent space via the forward method.
al.,
We also briefly compare VAEs and normalizing flows (obyzev et al. 2020 as both models map designs to latent spaces and back. While VAEs rely on learned encoder-decoder architecture, normalizing flows use carefully designed invertible operators to establish one-to-one correspondence between the latent and input spaces. Lee ct al.) 2025) observes that this invertibility effectively mitigates the reconstruction gap often seen in VA which can cause properly discrepancies between original and reconstructed designs. Consequently, they propose normalizing flow model for MBO, including the SeqFlow variant for sequence designs, to address those issues directly. Although the application of normalizing flows in offline MBO remains relatively limited, they represent a promising direction for future research.
5.2 Generative Adversarial Network (GAN)
General Principle Generative Adversarial Networks (GANs) introduce adversarial training framework in which generator network Go(z) and a discriminator network (2x)) compete against each other (Goodfellow et al., 2014). The generator maps noise z (sampled from a simple distribution, such as N I)) into the data space, while the discriminator attempts to distinguish real data from generated samples. The standard training loss is formulated as a minimax game:
min max Ex-pinns (m) [log (x) + Ez~p(z) [log(1 (G +
Conditional Generation GAN-based conditional generation is typically achieved via inverse methods, owing to the absence of an inherent latent code in standard GANs. In such frameworks, both the generator and discriminator are conditioned on target labels to steer the sampling process. For instance, Kumar & Levine (2020) employs a conditional GAN where the discriminator, parameterized as Dw a y), is trained output for valid (x.y) y) pairs (i.c., when comes from the data and y = f(x)) and 0 for generated pairs (Go(2.0) v), v). Here, the generator acts as the inverse mapping Go(2,)) y), taking both the latent noise and
21

---

Published in Transactions on Machine Learning Research (01/2026)
the condition label y imputs. This setup is optimized using the following objective:
min max Lp(D) Byno(u) (el log (x w)] + (x)) 108 D&s (Go(z.u) v) ] (9)
This formulation corresponds to matching the true conditional distribution po(æ y) with the model distribution (a. y) (obtained by marginaliving over 2). During guided sampling, for given larget y; the latent variable first sampled and then optimized such that the output of the forward model, fo (Z.G)zz))) closely approximates y. This process quantifies the agreement between the lcarned inverse map and an independently trained forward model fø, ensuring that the generated sample Go(z, v) not only satisfies the desired condition but also lies on the valid data manifold. Importance reweighting is also employed to construct a p(y) that assigns high probability to high y values.
Besides these inverse methods, the discriminator of GANs oflen utilized to detect whether a design is out-of-distribution (OOD), thereby regulating the optimization process of surrogate models (Qi et al. 2022 Yao et al. 2024a). Although both surrogate models and generative models have been explored in this context, these methods are technically not GAN-based forward methods, as they do not optimize the latent code within the GAN framework but rather use the discriminator to regularize the behavior of surrogate models.
5.3
Autoregressive Model
General Principle Autoregressive models are widely adopted for generative tasks, particularly in language modeling. Notable examples include LSTMs (Hochreiter 1997) and Transformer based models (Vaswani et al.
2017 Brown et al. 2020). which factorize the joint distribution an autoregressive manner.
Conditional Generation Latent representations for the design exist within autoregressive models, enabling forward methods that manipulate these latents via gradient optimization. For example, Dathathri et al. (2020) proposes using gradients from a surrogate model to adjust the language model's hidden activations, thereby guiding the generation process. However, directly manipulating these latent representations is not widely adopted, likely because design properties depend on the sequence as whole; modifying a token's 's latent representation without accounting for subsequent tokens can be less robust.
In autoregressive models, inverse methods are commonly applied and can be categorized into two types. The first type models a single sequence design, a stratogy often employed in biological sequence design. For instance, Angermiller et al. (2020) utilizes an autoregressive model for biological sequences, using a surrogate as reward and applying reinforcement learning to generate high-performing sequences. Similarly, Kim et al. (2023) employs an LSTM-based autoregressive model to generate biological sequences, then re-trains the generator using synthetic data labeled by the surrogate, assigning higher sample weights to high-performing synthetic sequences during training.
The second type models a sequence of designs and labels, aiming to capture the relationship between designs. In this line, Nguyen el al. (2023 pre-trains an autoregressive transformer on related and synthetic datasets and performs in-context learning by providing the offline dataset as context. A high-score label ye is then used as query to guide design generation. Additionally, Mashkaria et al. (2023) constructs a trajectory datasct by sorting samples based on score and trains an autoregressive model on this trajectory. During sampling, the model generates candidate points by rolling out trajectory that implicitly serves as the condition yes thereby guiding the generation process in an inverse manner.
5.4 Diffusion Model
General Principle Diffusion models, a subset of latent variable models, gradually perturb data by injecting Gaussian noise during the forward process. The reverse process iteratively denoises the data using a learned score estimator (Ho et al. 2020). The score function is approximated using a time-dependent neural network so s0 t), which facilitates the transformation of noise back into samples. They have demonstrated exceptional performance in synthesizing high-fidelity images and wide range of complex data types.
22

---

Published in Transactions on Machine Learning Research (01/2026)
Conditional Generation Conditional generation in diffusion models has been extensively studied and can also be broadly classified into two categories: inverse methods and forward methods.
In inverse methods, the conditional diffusion model is trained using either vanilla guidance, where the label or condition is directly provided as an input (Chang et al. 2025), or classifier-free guidance, which derives guidance by contrasting the outputs of a conditional model with those of an unconditional model (Ho & Salimans) (022). For example, Zhang et al. (2024) proposes a vanilla guidance approach that learns a weight function to assign higher weights to high-performing designs. This method focuses the training of the diffusion model sy go(Zz,ze)
figh-performing designs, using them implicit high-performing conditions Ve during sampling. However, vanilla guidance lacks an adjustable parameter to control sampling strength, which motivates the use of classifier-free guidance where the strength can be tuned via a parameter w. The corresponding score function is defined as follows:
$8 (z We) (1 + ww) Ve) - wSg(x)).
(10)
Krishnamoorthy et al. 2023) successfully apply classifier-free guidance to offline MBO by inputting the maximum value Ye from the offline dataset to produce high-performing designs. Building on this, Chen et al.] (2024) explore using surrogate model to guide the parameter w. Similarly, Yun et al. (2024) extend the method by incorporating not only the target property ye but also the entire trajectory into the conditional model to steer generation. In another work, Dao et al. (2025) generate synthetic data and train diffusion models to map low-performance samples to high-performmig designs; during sampling, the offline samples serve as initial samples and the diffusion model progressively guides them loward higher-performance designs.
In contrast, forward methods such as classifier guidance (Dhariwal & Nichol 2021 employ a surrogate model to steer the sampling process. The score function for classifier guidance is given by:
Ba (2 Mes w)) = sx(xx)) + WV, logPo (Vo (x))
(11)
In this context, Lee et al. (2023) investigate guided molecule generation toward high-performing regions with respect to target properties such as protein-ligand interactions, drug-likenes:, and synthesizability. In Yuan et al. 2024), gradient ascent is first employed to optimize the design. To address potential out-of-distribution issues, the method subsequently recovers the corresponding latent representation by injecting diffussin noise and then applying a denoising procedure, yielding a sample that conforms to the diffusion prior. This approach can be interpreted as a variant of classifier guidance due to its use of classifier gradient. Compared to classificr-free guidance, classifier guidance less frequently adopted, likely due to the additional training cost of an extra surrogate model and the polential risk of reward hacking associated with the classifier.
5.5 Flow Matching
General Principle Flow matching learns a vector field u(x: t) that defines a deterministic flow by solving ordinary differential equation (Lipman et al. 2023 Le et al. 2023) Notably, v(æ, t) can be used to derive the score Va log.oe(( (2 and vice versa (scc Lemma in Zheng et al. (2023)) ). This demonstrates that diffusion models and flow matching follow the same probability path under certain constraints.
Conditional Generation Because flow matching closely resembles diffussio models, analogous conditional generation techniques can be applied. In particular, both inverse method classifier-free guidance (Zheng et al. 2023 and forward method classifier guidance (Dao et al. 2023) are readily adaptable within the flow matching framework. Regarding the inverse method, Stärk et al. (2024) introduce Dirichlet flow matching on the simplex and extend classifier-free guidance to more effectively steer the sequence generation process. In the forward method, Yuan et al. (2025) investigate the use of multiple surrogate models to guide flow sampling toward the Parcto-front in multi-objective optimization settings, with empirical results indicating superior performance over diffusion models (Yao et al.) 2024b). Moreover, Chen et al. 2025 propose training an affinity predictor to steer protein conformation sampling toward stable configurations within the AlphaFlow framework (Jing et al. 2024h.
Given flow matching's emerging success and its demonstrated advantages in performance and efficiency over diffusion models, anticipate a surge in research exploring its applications to offline MBO.
23

---

Published in Transactions on Machine Learning Research (01/2026)
5.6 Energy- Energy-Based Model
General Principle Bnergy-bused Models (EBMs) define an unnormalized probability distribution over data via an energy function Ea(x) (LCCnn et al. 2006):
pe(x) exp (x)
((0)
where Z(0) denotes the partition function. Training EBMs typically aims to assign lower energy observed data while raising the energy of samples drawn from the model. A common objective is contrastive divergence which encourages the model to distinguish between real data and generated (negative) samples. Sampling from an EBM is challenging due to the intractability of the partition function, and it generally relies on Markov Chain Monte Carlo (MCMC) techniques (Neal 1993:
Hinton 2002
Tieleman 2008).
We note that GelowNets (Bengio et al., 2023 can amortize the MCMC process, making them applicable to EBMs (Zhang et al.] 2022). Although these methods enable faster mode mixing to estimate the partition function to compare with MCMC met hods, thus improving the practicality of EBMs, none of these techniques have been applied to offline black-bor optimization. We believe that exploring this direction could offer promising avenues for future research.
Conditional Generation Conditional generation in the context of EBMs can similarly be classified into inverse and forward methods. For instance, Frey et al. (2024) maps protein sequences into a latent space during an initial jump step and trains an EBM on this latent representation assigning lower energy to observed data while penalizing generated samples with higher energy. In the subsequent walk step, Langevin MCMC is employed to sample new latent codes, with binary projection matrix ensuring that specified regions of the sequence remain unchanged.
Similarly, Yu et al. (2024) introduces a method that jointly embeds design and properties into a compact yet expressive muergy-bases latent space. In this approach, the highest offline dataset score, yes is used to sample latent code z, which then decoded to yield the design æ. We categorize this method as forward, since the sampling of z is governed by
p(z Ve) x po 2) po (Me 12),
with explicitly modeled surrogate whose gradient is leveraged via SVGD Liu & Wang 2016
It is important to note that the distinction between forward and inverse methods in EBMs is often subtle, as both the energy function and a surrogate model essentially map a design to a scalar value. In Beckham & Pal (0023). the authors reinterpret the original forward method, conservative objective models (COMs), as an EBM trained via contrastive divergence. COMs optimizes two losses-a a mcan mean-squared error loss for surrogate modeling and a conservative objective for the EBM EBM-using shared network architecture, where the resulting energy function steers the sampling process towards high-performing designs, characteristic typically associated with inverse methods. Moreover, [Beckham & Pal (2023) further proposes a decoupled version of COMs, in which separate networks are employed for the surrogate and the EBM, reinforcing its classification as a forward method.
5.7 Control by Generative Flow Network (GFlowNet)
Unlike earlier sections on general generative models and their conditional approaches, this section introduces a control method: Generative Flow Networks (GFlowNets) (Bengio et al., 2021 2023 GFlowNets model generation as sequential decision process, where a solution z is constructed through trajectory of transitions. Their goal is amortized inference maferince-sampling from a distribution proportional to a reward function, p(x) R(x). This produces samples that are both high-reward and diversc, which is ospecially important when the reward is an imperfect surrogate learned from ofllin data. Unlike standard RL, which focuses on maximizing R(x) and may be unsafe under epistemic uncertainty, GFlowNets balance exploration and exploitation, making them attractive in offline black-box optimization. A sample is generated by traversing a directed acyclic graph from an initial state sy to a terminal state $T x::
80
81
ST.
24

---

Published in Transactions on Machine Learning Research (01/2026)
Training is based the flow consistency condition: for any intermediate state s', incoming flow equals outgoing flow,
Σ
0(s;0) Pr(s') 0; F(s':0),
*EPrentts("")
with terminal flow fixed to the reward,
F(sr; 0) R(a:).
Different training objectives instantiate this principle, including trajectory balance (TB) (Malkin et al. 2022 and sub-trajectory balance (SubTB) (Madan et al.) 2023). These objectives have been used to control diverse generative models, including molecular graphs (Bengio et al. 2021), bidirectional string models (Kim et al., 2024ch, and diffusion models (Lahlou et al. 2023a).
Offline MBO applications During sampling, GFlowNet sequentially selects transitions based on its learned policy until reaching terminal state æ. This sequential framework is particularly effective for exploring high-dimensinn -isensiienson spaces and generating diverse candidate solutions. In offline MBO, guided sampling via GFlowNets is especially natural.
For example, Jain et al. 2022 generates desirable biological sequences from scratch by defining a target reward function as the upper confidence bound score from a surrogate model. To improve robustness against the imperfections of the surrogate model at early stages, Kim et al. (2024a) conservatively search promising regions by introducing parameter 8, which is adjusted based on the prediction model's uncertainty.
Additionally, Ghari et al. (2023) utilize GFlowNets to modily existing sequences to enhance target properties, while Jain et al. (2023) employ conditional GFlowNets to generate diverse Pareto-optimal solutions for multi-objective optimization problems. Note that they use autorogrossive modols to produce these biological sequences and employ GFlowNets to control them effectively.
One of the main challenges in offline black-box optimization is the apploration-expliiaatiii trade-off. Unlike RL, GFlowNets p(x(3) & R(x)². Kim et al. (2024b) propose an effective way to learn such policy by introducing logit scaling network and verify that it achieves high extrapolation ability in offline black-box optimization tasks. They use directional token generative models, which can generate sequences by prepending or appending tokens, and employ GFlowNets to control them.
effectively balance exploration and exploitation using temperature parameter B, i.c.,
We can also formulate the offline black-box optimization problem as posterior inference, where we have a pre-trained policy p(æ) and a reward function R(x)) trained on a given dataset. In this setting, we can use the RTB loss to obtain unbiased sampler that amortizes the posterior distribution. For example, Yun et al. (025)) propose posterior inference method with GFlowNets for diffusion models in black-box online blx optimization. This work may provide a key insight for applying posterior inference with GFlowNets to offline black-box optimization.
Comparison of Generative Models in Offline MBO. We have presented a range of generative models used in offline MBO. Below, we summarize their respective strengths and limitations in this context.
Variational autoencoders provide a continuous, differentiable latent space suitable for gradient-bascd offline MBO, but they can suffer from posterior collapse and reconstruction mismatch that may lead to inaccurate property estimates.
Generative adversarial networks generate high-quality samples but typically lack an explicit latent space for controllable optimization, often requiring inverse methods. Additionally, training be unstable due to mode collapse. The GAN discriminator is frequently used to detect out-t--distribution (OOD) designs.
Autoregressive models are well-suited for sequence generation and are often combined with reinforcement learning techniques for guided sampling, though the sequential sampling process is inherently slow.
Diffusion models provide stable training, high sample fidelity, and natural diversity. They are computation- ally intensive at inference time due to their iterative denoising process, but both classifier and classifier-free guidance strategies have been effectively adapted to offline MBO.
25

---

Published in Transactions on Machine Learning Research (01/2026)
Flow matching shares many benefits with diffusion models but offers improved efficiency and performance.
EBMs are uniquely valuable in offline MBO for their ability to naturally penalize out-of-distribution samples and flexibly encode complex, domain-specifie objectives. However, they are limited by slow MCMC-based sampling and unstable training dynamics.
GFlowNets, as control framework, are particularly well-suited for offine MBO due to their ability to generate diverse, high-reward solutions and explore safely under uncertainty, though training cost is relatively high due to flow consistency constraints.
Practical Guide on Selecting Generative Models. We have discussed various generative models. The choice of an appropriate model primarily depends the data modality. Each type of data typically has community-endorreee
state-of-the-an generative model. For instance, when the design is a prompt and the black-box property is the downstream task performance of an LLM given that prompt, autoregressive GPT-style models are the dominant choice due to strong empirical performances (Ynng et al. 2024). Similarly, when the design is an image and the larget property is a fine-grained visual altribule (e.g., a specific hairstyle), diffusion models are preferred for their superior image generation capabilities (Dhariwal & Nichol 2021
While model selection is primarily guided by data modality, this does not diminish the importance of discussing conditional generation stralegies across different model families. In offline MBO, each generative model typically requires a tailored conditioning approach. For example, RGD (Chen et al.) 2024) exploits the probability flow ODE of diffusion models to derive a refined proxy distribution and optimize the strength parameter an approach unique to diffusion models. Similarly, MIN (Kumar Levine, 2020) utilizes a GAN to directly map high-scoring property values candidate designs through one-step generation, optimizing the values via a forward-inverse consistency loss, which is incompatible with the multi-step sampling process of diffusion models. Furthermore, certain models like VAEs support latent code manipulation, a feature generally unavailable in standard GANs due to the lack of an explicit latent eppresentation.
There are cases where multiple generative models perform well for the same data modality. Protein sequence design is a representative example, and it is one of the most extensively studied tasks in offline MBO. In this setting, both autoregressive (AR) models (Elnaggar et al. 2021) and diffusion models (Wang et al., 2024 have demonstratod strong empirical performance. When deciding between the two, several additional considerations become important:
Likelihood estimation: Offline MBO often requires estimating the likelihood of candidate designs to detect and avoid out-of-distribution (OOD) samples. AR models can compute exact. likelihoods by factorizing the joint distribution into conditional probabilities. In contrast, diffusion models rely on variational approximations such as the ELBO, which is computationally challenging. Thus, when precise likelihood computation and rigorous OOD detection are essential, AR models are generally preferred.
Sample diversity: Generating diverse samples is crucial for effective exploration in ofline MBO. Diffusion models naturally provide broader mode coverage compared to AR models, making them better suited for tasks where diversity and exploration are prioritized.
Sample manipulation: The ability to perform localized edits on generated samples is critically important for control in offline MBO. Diffusion models support such fine-grained manipulation through their iterative denoising process. For instance, in antibody desigu, diffusson models can selectively generate CDR regions while preserving the antibody framework (Luo et al. 2022) - capability not easily realized with AR models. Moreover, diffusion models benefit from their bidirectional nature (conditioning on both past and future context) and are compatible with advanced guided sampling techniques, enabling more flexible and nuanced control. A trade-off, however, is that diffusion models often have a fixed sequence length, whereas AR models natively support variable-length generation.
Availability of pretrained models: Practical deployment is often influenced by the accessibility of strong pretrained models. Fortunately, both AR (Elnaggar et al.) 2021 and diffusion (Wang et al., 2024 models are publicly available and widely used. Leveraging these publicly available models can help mitigate OOD issues effectively.
26

---

Published in Transactions on Machine Learning Research (01/2026)
Efficient sampling is essential for scaling offine MBO to large candidate sets. AR models generate sequences token by token and are generally faster for shorter sequences. Diffusion models denoise entire sequences over multiple steps, which can be more efficient for longer sequences, though their overall speed depends on the number of denoising iterations used.
Sampling efficiency:
Summary: In offline MBO for prolein sequence design, diffusion models may be more suitable due to their superior sample diversity and manipulability, despite limitations in exact likelihood estimation.
6 Discussion and Future Direction
In this paper, we present a comprchensive review of offline MBO. Despite significant efforts to develop robust surrogate models and generative models, many practical challenges remain. Offline MBO is inherently difficult due to the limited availability of offline datasets and the epistemic uncertainty that plagues surrogate models. In this section, we outline promising future research directions aimed at addressing these challenges, including the development of more rigorous benchmarks, improved uncertainty estimation methods, innovative graphical modeling approaches for surrogate modeling, advanced generative modeling techniques, and high-impact applications in LLM alignment and AI safety.
Robust and Realistic Benchmarking on Scientific Design Current scientific design benchmarks in offline MBO face two major challenges. First, due to the difficulty of collecting labeled data, some benchmarks- such as TFB8 and TFB10 (Barrera et al. 2016) offer overly constrained search spaces where even simple gradient ascent methods can achieve impressive results, making difficult to distinguish the performance of more sophisticated algorithms. Sccond, benchmarks like superconductor (Hamidich, 2018) often rely on learned oracles for evaluation, which can be vulnerable to manipulation and may not accurately reflect true performance. Moving forward, it is essential to develop benchmarks that not only present more challenging scarch spaces but also incorporate reliable evaluation protocols that are resistant to exploitation.
Uncertainty Estimation of Surrogate Model In offline black-box optimization, capturing the significant epistemic uncertainty in surrogate models is paramount, especially because identifying which inputs drive this uncertainty remains a core challenge. While uncertainty estimation is similarly important in online black-box optimization, in offline scenarios it is even more critical for preventing reward hacking, as one cannot correct for flawed model predictions through active data collection. Various tochniques- as adversarial regularization (Trabucco al., 2021), smoothness priors (Yu et al. 2021a), and kernel-based methods (Chen et al., 2022b) have been proposed to mitigate uncertainty and ensure safer optimization; however, there has been comparatively little focus leveraging Bayesian methods for directly quantifying epistemic uncertainty. Moreover, existing benchmarks often emphasize overall optimization performance without clarifying whether observed gains stem from superior surrogate modeling, improved optimization strategies, or mere chance. This lack distinction underscores the need for independent and rigorous ovaluations of the uncertainty estimation capabilitics of the surrogate model in newly developed algorithms.
Although recent efforts such as .Jain al. (2022) using Monte Carlo (MC) dropout (Gal & Ghahramani] 2016) and deep ensembles (Takshminarayanan et al. 2017), and Kim et al. (2024a) incorporating uncertainty measures for conservative search have made inroads into this area, they still fall short of providing robust solution. Consequently, advancing offline MBO demands a fundamentally stronger approach to uncertainty quantification that transcends basic MC dropout or ensembling techniques.
Future work may build upon this line of research by exploring recent methodologies such as:
DEUP: Direct Epistemic Uncertainty Prediction Lahhlou et al. 2023b): This approach directly estimates the excess risk associated with model misspecification by learning secondary predictor for generalization error, offering a more principled uncertainty measure.
Efficient Variational Inference Methods over Neural Network Parameters: Efficient variational inference methods offer promising solutions for tackling the intractable posterior inference in neural networks. For example, the Variational Bayesian Last Layer (VBLL) approach (Harrison et al. 2024
27

---

Published in Transactions on Machine Learning Research (01/2026)
performs inference solely on the final layer, reducing the computational complexity to a quadratic level. Similarly, GFlowOut, introduced by Liu et al. (2023), leverages GFlowNets form of hierarchical variational inference (Malkin et al. 2023) to approximate the posterior distribution over dropout masks, effectively addressing challenges related to multi-modality and sample dependency. Together, these methods represent compelling candidates for enhancing uncertainly estimation surrogate models while maintaining computational efficiency.
Deep kernels, which leverage deep architectures to learn expressive kernel functions, offer a scalable alternative to Gaussian processes (Wilson et al. 2016 Liu et al.) 2020p. They have been applied to biological sequence design scenarios by employing a denoising autocncoder to learn a discriminative deep kernel GP for Bayesian optimization of biological sequences (Stanton et al.) 2022). This approach was further refined by Grrvver et al. (2023), who used a discrete diffusion model and simple last-layer ensemble techniques to evaluate uncertainty. These successes in online black-box optimization could be directly transferred to offline MBO, where uncertainty estimation helps prevent reward hacking. Such a strategy could effectively combine existing surrogate modeling and generative modeling methods in offline MBO fields.
Deep Kernels:
Graphical Surrogate Model Offline surrogate models often suffer from limited data coverage, making them vulnerable to overestimation and reward hacking in regions outside the offline distribution. A promis- ing mitigation strategy is to leverage factorized graphical models such as Functional Graphical Models (FGMs) (Kuba et al.] 2024b)-15 to docompose high-dimensional function into a sum of local subfunctions defined over smaller cliques. This structured factorization enables each subeomponent to be learned from a subspace with denser data coverage, thereby localizing distribution shifts and enhancing both robustness and OOD generalization ŞKuba et al. 2024a). In addition to FGMs, candidate methods for graph discovery such as those based on GFlowNets -ofee alternative avenues to uncover latent causal structures (Deleu et al. 2022). Employing such graphical discovery methods will provide a principled means to address distributional shifts in offline MBO, ultimately leading to more reliable optimization outcomes under limited data coverage.
Advanced Gencrative Modcling Many existing offline MBO methods employ relatively simplistic generative models. For instance, several approaches use basic encoder-decoder erchitectures that map protein sequences into a latent logit space for optimization (Trabucco et al.) 2022). While such methods capture general machine learning principles, they often overlook the rich biophysical information embedded in the data. In applicatious like protein design, it is crucial to leverage models that integrate domain-specific knowledge-suin such as pre-trained language models or struct ure-aware representations- to more accurately model the underlying data distribution (Watson et al. 2023). By developing generative models that are tailored to the unique characteristics of the target domain, future methods can achieve not only improved optimization performance but also greater interpretability and robustness in real-world applications.
A Application to LLM Alignment. and AI Safety While offline MBO has traditionally been applied to design tasks in fields such as biology or chemistry, its mothodologics can also potentially inform post-training strategies for large language models (LLMs). Approaches like supervised fine-tuning (SFT), RLHF (Ouyang et al. 2022). or RL-based reasoning (Guo et al., 2025), aim to enhance text generation by leveraging reward signals derived from human preference models or other evaluative metrics. Because these reward models are inherently uncertain and prone to reward hacking, adopting the conservative and safe optimization techniques developed in offline MBO may help mitigate such risks. Looking forward, we speculate that insights from offline MBO's robust optimization principles may also inform future directions in ensuring the safety and reliability of increasingly capable LLMs (Bengio et al. 2025).
Acknowledgement
This research is partially supported by the Fonds de recherche du Québec Nature et tochnologics, as well as funding from Samsung, CIFAR, the CIFAR AI Chair program, and the Canadian AI Safety Institute Research Program at CIFAR through Catalyst award. Minsu Kim acknowledges funding from the KAIST
28

---

Published in Transactions on Machine Learning Research (01/2026)
Jang Young Sil Fellow Program. We sincerely thank Moksh Jain from Mila and Brandon Trabucco from CMU for insightful discussions.
References
Michael Ahn, Henry Zhu, Kristian Hartikainen, Hugo Ponte, Abhishek Gupta, Sergey Levine, and Vikash Kumar. Robel: robotics benchmarks for learning with low-cost robots. In Conference on Robot Learning (CoRL), 2020.
Rebecca F. Alford, Andrew Leaver-Fay, Jeliazko R. Jeliazkov, Matthew J. O'Meara, Frank P. DiMaio, Hahnbeom Park, Maxim V. Shapovalov, P. Douglas Renfrew, Vikram K. Mulligan, Kalli Kappel, Jason W. Labonte, Michael S. Pacella, Richard Bonneau, Philip Bradley, Roland L. Dunbrack Jr., Rhiju Das, David Baker, Brian Kuhlman, Tanja Kortemme, and Jeffrey J. Gray. The rosetta all-atom energy function for macromolecular modeling and design. Journal of Chemical Theory and Computation, 2017.
Hossain M. Amir and Takashi Hascgawa. Nonlincar mixed-discrete structural optimization. Journal of Structural Engineering, 115, 1989.
Christof Angermüller,, David Dohan, David Belanger, Ramya Deshpande, Kevin Murphy, and Lucy Colwell. Model-based reinforcement. learning for biological sequence design. In 8th International Conference on Learning Representations, ICLR 2020, Addis Ababa, Ethiopia, April 26-30, 2020. OpenReeiew.net, 2020.
Luis A Barrera, Anastasia Vodenko, Jesse V Kurland, Julia M Rogers, Stephen S Gisselbrecht, Elizabeth J Rossin, Jaie Woodard, Luca Mariani, Kian Hong Kock, Sachi Inukai, Trevor Siggers, Leila Shokri, Raluca Gordân, Nidhi Sahni, Chris Cotsapas, Tong Hao, Song Yi, Manolis Kellis, Mark J Daly, Marc Vidal, David E Hill, and Martha L Bulyk. Survey of variation in human transcription factors reveals prevalent. DNA binding changes. Science, 351, 2016.
Christopher Beckham and Christopher Pal. Conservative objective models are special kind of rastivvvvve divergence-based energy model. arXiv preprint arxi::2304.038 03866, 2023.
Christopher Beckham, Alexandre Piché, David Vazquez, and Christopher Pal. Exploring validation metrics for offline model-based optimisation with diffusion models. Transactions on Machine Learning Research, 2024.
Emmanuel Bengio, Moksh Jain, Maksym Korablyov, Doina Precup, and Yoshua Bengio. Flow network based generative models for non-iterative diverse candidate generation. In Mare' Aurclio Ranzato, Alina Beygelzimer, Yann N. Dauphin, Percy Liang, and Jennifer Wortman Vaughan (eds.), Advonces in Neural Information Processing Systems 34: Annual Conference Neural Information Processing Systems 2021, NeurlPS 2021, December 6-14, 2021, virtual, pp. 17394,, 2021.
Yoshua Bengio, Nicholas Léonard, and Aaron Courville. Estimating or propagating gradients through stochastic neurons for conditional computation. arXiv preprint urXiv:1308.3432 2013.
Yoshua Bengio, Salem Lahlou, Tristan Deleu, Edward Hu, Mo Tiwari, and Emmanuel Bengio. Gflownet foundations. The Journal of Machine Learning Research, 24, 2023.
Yoshua Bengio, Michael Cohen, Damiano Fornasiere, Joumana Ghosn, Pietro Greiner, Matt MacDermott, Sören Mindermann, Adam Oberman, Jesse Richardson, Oliver Richardson, Marc-Antoine Rondeau, Pierre- Lue St-Charles, and David Williams-King, Superintelligent agents pose catastrophic risks: Can scientist ai offer a safer path? arXiv preprint arXim:2502.150 15657, 2025.
Julian Blank and Kalyanmoy Deb. Pymoo: Multi-objective optimization in python. 1EEE Access, 8: 89497 89509, 2020.
P.A.N. Bosman and D. Thierens. The balance between proximity and diversity in multiobjective evolutionary algorithms. IEF. Transactions Evolutionary Computation, 7, 2003.
29

---

Published in Transactions on Machine Learning Research (01/2026)
Greg Brockman, Vicki Cheung, Ludwig Pettersson, Jonas Schneider, John Schulman, Jie Tang, and Wojeiech Zaremba. Openai gym. arXiv preprint or orxi::166..c 015600 2016.
David H. Brookes, Hahnbeom Park, and Jennifer Listgarten. Conditioning by adaptive sampling for robust design. In Kamalika Chaudhuri and Ruslan Salakhutdinov (eds.), Proceedings of the 36th International Conference on Machine Learning, ICML 2019, 9-15 June 2019, Long Beach, California, USA, volume 97
of Proceedings of Machine Learning Research, pp. 773-782. PMLR, 2019.
Nathan Brown, Marco Fiscato, Marwin HS Segler, and Alain C Vaucher. Guacamol: benchmarking models for de novo molecular design. Journal of Chemical Information and Modeling, 59, 2019.
Tom B. Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared Kaplan, Prafulla Dhariwal, Arvind Neclakantan, Pranav Shyam, Girish Sastry, Amanda Askell, Sandhini Agarwal, Ariel Herbert-Voss Gretchen Krueger, Tom Henighan, Rewon Child, Aditya Ramesh, Daniel M. Ziegler, Jeffrey Wu, Clemens Winter, Christopher Hesse, Mark Chen, Eric Sigler, Mateusz Litwin, Scott Gray, Benjamin Chess, Jack Clark, Christopher Berner, Sam McCandlish, Alec Radford, lyya Sutskever, and Dario Amodei. Language models are few-shot learners. In Hugo Larochelle, Marc' Aurclio Ranzato, Raia Hadsell, Maria-Florina Balcan, and Hsuan-Tien Lin (eds.). Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, NewrIPS 2020, December 6-12, 2020, virtual, 2020.
Ziyi Chang, George A. Koulieris, Hyung Jin Chang, and Hubert P.H. Shum. On the design fundamentals of diffusion models: A survey. Pattern Recognition, 169(C), 2025.
Yassine Chemingui, Aryan Deshwal, Trong Nghia Hoang, and Janardhan Rao Doppa. Offline model-based optimization via policy-guides gradient scarch. In Michael J. Wooldridge, Jemnifer G. Dy, and Sriraam Natarajan (eds.), Thirly-Eighill AAAI Conference on Artificial Intelligence, AAAI 2024, ThirlySSidh Sicth Conference on Innovative Applications of Artificiol Intelligence, IAAI 2024, Fourteenth Symposium on Educational Advances in Artificial Intelligence, EAAI 2014, February 20-27, 2024, Vancouver, Canada, pp. 11230-11233 AAAI Press, 2024. doi: 10.1609/aaae htt///aai.v..i...... v38i10.29001.
Can Chen, Xi Chen, Chen Ma, Zixuan Liu, and Xue Liu. Gradient-based bi-level optimization for deep learning: A survey. arXiv preprint arXiv:2207. 11719, 2022a.
Can Chen, Yingxue Zhang, Jie Fu, Xue (Steve) Liu, and Mark Coates. Bidirectional learning for offline infinite-width model-based optimization. In Sanmi Koyejo, S. Mohamed, A. Agarwal, Danielle Belgrave, K. Cho, and A. Oh (eds.). Advances in Neural Information Processing Systems 35: Annual Conference Neural Information Processing Systems 2022, NewrIPS 2022, New Orleans, LA, USA, November 28- December 9, 2022, 2022b.
Can Chen, Christopher Beckham, Zixuan Liu, Xue (Steve) Liu, and Chris Pal.
for offline model-based optimization. In Alice Oh, Tristan Naumann, Amir Globerson, Kate Saenko, Moritz Hardt, and Sergey Levine (eds.), Advances in Neural Information Processing Systems 36: Annual Conference on Neural Information Processing Systems 2023, NewrIPS 2023, New Orleans, LA, USA, December 10 16, 2023, 2023a.
Can Chen, Yingxue Zhang, Xue Liu, and Mark Coates. Bidirectional learning for offline mosel biological sequence design. In Andreas Krause, Emma Brunskill, Kyunghyun Cho, Barbara Engelhardt, Sivan Sabato, and Jonathan Scarlett (ods.), International Conference on Machine Learning, ICML 2029, 23-29 July 2023, Honolulu, Hawati, USA, volume 202 of Proceedings of Machine Learning Research, pp. 5351 5366. PMLR, 2023b.
Can Chen, Jingbo Zhou, Fan Wang, Xue Liu, and Dejing Dou. Structure-aware protein sule-super learning. Bioinformatics, 39, 2023c.
Can Chen, Christopher Beckham, Zixuan Liu, Xue Liu, and Christopher Pal. Robust guided diffusion for offline black-box optimization. Transactions on Machine Learning Research, 2024.
30

---

Published in Transactions on Machine Learning Research (01/2026)
Can Chen, Karla-Luise Herpoldt, Chenchao Zhao, Zichen Wang, Marcus Collins, Shang Shang, and Ron Benson. Affinityflow: Guided flows for antibody affinity maturation. In International Conference on Machine Learning, 1CML 2025, 13-19 July 2025, Vancouver, BC, Canada, Proceedings of Machine Learning Research. PMLR, 2025.
Zhao Chen, Vijay Badrinarayanan, Chen- Yu Lee, and Andrew Rabinovich. Gradnorm: Gradient normalization for adaptive loss balancing in deep multitask networks. In Jennifer G. Dy and Andreas Krause (eds.), Proceedings of the 35th International Conference on Machine Learning, 1CML 2018, Stockholmsmässan, Slockholm, Sweden, July 10-15, 2018, volune 80 of Proceedings of Machine Learning Research, pp. 793 802. PMLR, 2018.
Franklin Y. Cheng and X. S. Li. Generalized center method for multiobjective engineering optimization. Engincering Optimization, 31, 1999.
C A Coello Coello and G T Pulido. Multiobjective structural optimization using a microgenetic algorithm. Structural and Multidisciplnary Oplimization, 30, 2005.
Farhan Damani, David Brookes, Theodore Sternlieb, Cameron Webster, Stephen Malina, Rishi Jajoo, Kathy Lin, and Sam Sinai. Beyond the training sct: an intuitive method for detecting distribution shift model-based optimization. arXiv preprint orXiv:2311.05363 2023.
Steven J. Daniels, Alma A. M. Rahat, Richard M. Everson, Gavin R. Tabor, and Jonathan E. Fieldsend. A suite of computationally expensive shape optimisation problems using computational fluid dynamics. In Parallel Problem Solving from Nature PPSN XV. Springer International Publishing, 2018.
Cuong Dao, Phi Le Nguyen, Truong Thao Nguyen, and Nghia Hoang. Incorporating surrogate gradient norm to improve offline optimization techniques. In Amir Globersons, Lester Mackey, Danielle Belgrave, Angela Fan, Urrih Paquet, Jakub M. Tomczak, and Cheng Zhang (eds.), Advances in Neural Information Processing Systems 38: Anneual Conference on Neural Information Processing Systems 2024, NewrIPS 2024, Vancouver, BC, Canada, December 10- 15, 2024, 2024a.
Manh Cuong Dao, Phi Le Nguyen, Thao Nguyen Truong, and Trong Nghia Hoang. Boosting offline optimizers with surrogate sensitivity. In Ruslan Salakhutdinov, Zico Kolter, Katherine Heller, Adrian Weller, Nuria Oliver, Jonathan Scarlett, and Felix Berkenkamp (eds.), Proceedings of the 41st International Conference Machine Learning, volume 235 of Proceedings of Machine Learning Research, pp. 10072-10090. PMLR, 21 21-27 Jul 2024b.
Manh Cuong Dao, The Hung Tran, Phi Le Nguyen, Thao Nguyen Truong, and Trong Nghia Hoang. From Low To High-value Designs: Offline Optimization Via Generalized Diffusion, 2025.
Quan Dao, Hao Phung, Binh Nguyen, and Anh Tran. Flow matching latent space. ar preprinl arXiv:2307.08660 2023.
Sumanth Dathathri, Andrea Madotto, Janice Lan, Jane Hung, Eric Frank, Piero Molino, Jason Yosinski, and Rosanne Liu. Plug and play language models: A simple approach to controlled text generation. In 8th International Conference Leorning Representations, ICLR 2020, Addis Ababa, Ethiopia, April 26-30, 2020. OpenReview.net, 2020.
Kalyanmoy Deb and Himanshu Jain. An evolutionary many-objective optimization algorithm using reference- point-based nondominated sorting approach, part i: Solving problems with box constraints. IEEE Transactions on Evolutionary Computation, 18, 2014.
Kalyanmoy Deb and Aravind Srinivasan. Innovization: innovating design principles through optimization. Proceedings of The 8th Annual Conference on Genetic and Evolutionary Computation, 2006.
Kalyanmoy Deb and Santosh Tiwari. Omni-optimizer: A generic evolutionary algorithm for single and multi-objective optimization. European Journal of Operational Research, 185, 2008.
31

---

Published in Transactions on Machine Learning Research (01/2026)
Kalyanmoy Deb, Lothar Thiele, Marco Laumanns, and Eckart Zitzler. Scalable Test Problems for Ecolutionary Multiobjeclive Oplimization, pp. 105-145. Springer London, 2005.
Erick Delage and Yinyu Ye. Distributionally robust optimization under moment uncertainty with application to data-driven problems. Operations Research, (8(3):595-613 2010.
Tristan Deleu, António Góis, Chris Emezue, Mansi Rankawat, Simon Lacoste-Julien, Stefan Bauer, and Yoshua Bengio. Bayesian structure learning with generative flow networks. In James Cussens and Kun Zhang (eds.), Uncertainty in Artificial Intelligence, Proceedings of the Thirly- Harry--ighth Conference on Uncertainty in Artificial Intelligence, UAI 2022, 1-5 August 2022, Eindhoven, The Netherlands, volume 180 of Proceedings of Machine Learning Research, pp. 318-528. PMLR, 2022.
Armen Der Kiureghian and Ove Ditlevsen. Aleatory or epistemic? does it matter? Structural safety, 2009.
Jean-Antoine Désidéri. culttple-gradienn descent algorithm (mgda) for multiobjective optimization. Comptes Rendus Mathemalique, 350, 2012.
Prafulla Dhariwal and Alexander Quinn Nichol. Diffusion models beat gans on image synthesis. In Mare' Aurelio Ranzato, Alina Beygekzmer, Yann N. Dauphin, Percy Liang, and Jennifer Wortman Vaughan (eds.), Advonces in Neural Information Processing Systems 34: Annual Conference on Neural Information Processing Systems 2021, NewrIPS 2021, December 6-14, 2021, virtual, pp. 8780 8794, 2021.
Thomas G Dietterich. Ensemble methods in machine learning. In Multiple Classifier Systems: First International Workshop, 2000.
Katharina Eggensperger, Philipp Müller, Neeratyoy Mallik, Matthias Feurer, René Sass, Aaron Klein, Noor Awad, Marius Lindauer, and Frank Hutter. Hpobench: A collection of reproducible multi-fidelity benchmark problems for hpo, 2021.
Ahmed Elnaggar, Michael Heinzinger, Christian Dallago, Ghalia Rihawi, Yu Wang, Llion Jones, Tom Gibbs, Tamas Feher, Christoph Angerer, Martin Steinegger, Debsindhu Bhowmik, and Burkhard Rost. Prottrans: lowards cracking the language of life's code through self-supervised learning, IEEE Trunsactions on Pallern Analysis and Machine Intelligence, 44:7112-718 1217127 2021.
Clara Fannjiang and Jennifer Listgarten. Autofocused oracles for model-based design. In Hugo Larochelle, Mare' Aurelio Ranzato, Raia Hadsell, Maria-Florina Balcan, and Hsuan-Tien Lin (eds.), Advances in Newral Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, NewrIPS 2020, December 6-12, 2020, virtual, 2020.
A. Farhang- Mchr and Shapour Azarm. Eatropy-based multi-objective genetic algorithm for design optimization. Structural and Multidisciplinary Optimization, 24, 2002.
Peter I Frazier. A tutorial bayesian optimization. arXiv preprint arXio:1807.02811 2018.
Nathan C. Frey, Daniel Berenberg, Karina Zadorozhny, Joseph Kleinhenz, Julien Lafrance- Vanasse, Isidro Hötzel, Yan Wu, Stephen Ra, Richard Bonneau, Kyunghyun Cho, Andreas Loukas, Vladimir Gligorijevic, and Saeed Saremi. Protein discovery with discrete walk-jump sampling. In The Twelfth International Conference on Learning Representations, ICLR 2024, Vienna, Austria, May 7-11, 2024. OpenReview.net, 2024.
Nathan C. Frey, Isidro Hötzel, Samuel D. Stanton, Ryan Kelly, Robert G. Alberstein, Emily Makowski, Karolis Martinkus, Daniel Berenberg, Jack Bevers, Tyler Bryson, Pamela Chan, Alicja Czubaty, Tamica D'Souza, Henri Dwyer, Anna Dziewulska, James W. Fairman, Allen Goodman, Jennifer Hofmann, Henry Isaacson, Aya Ismail, Samantha James, Taylor Joren, Simon Kelow, James R. Kiefer, Matthicu Kirchmeyer, Joseph Kleinhenz, James T. Koerber, Julien Lafrance-Vannn Edith Lee, Donald Lee, Wei-Ching Liang, Joshua Yao Yu Lin, Sidney Lisanza, Andreas Loukas, Jan Ludwiczak, Sai Pooja Mahajan, Omar Mahmood, Homa Mohammadi-Poyhante Santrupti Nerli, Ji Won Park, Jaewoo Park, Stephen Ra, Sarah Robinson, Saced Saremi, Franziska Seeger, Imee Sinha, Anna M. Sokol, Natasa Tagasovska, Hao To, Edward Wagstaff, Amy Wang, Andrew M. Watkins, Blair Wilson,
Andrew Leaver-Fay, Jae Hyeon Lee,
32

---

Published in Transactions on Machine Learning Research (01/2026)
Shuang Wu, Karina Zadorozhny, John Marioni, Aviv Regev, Yan Wu, Kyunghyun Cho, Richard Bonneau, and Vladimir Gligorijevié. Lab-in-the-loop therapeutic antibody design with deep learning. RioRric preprinl 1tt.:::::...11120220022 02. 19960900,, 2025.
Justin Fu and Sergey Levine. Offline model-based optimization via normalized maximum likelihood estimation. In 9th International Conference Learning Representations, 1CLR 2021, Virtual Event, Austria, May 3-7, 2021. OpenReview.net, 2021.
Tianfan Fu, Wenhao Gao, Cao Xiao, Jacob Yasonik, Connor W Colcy, and Jimeng Sun. Differcntiable scaffold- ing tree for molecular optimization. In The Tenth International Conference on Learning Regresenlalions, ICLR 2022, Virtual Event, April 25-29, 2022. OpenReview.neg net, 2022.
Yarin Gal and Zoubin Ghahramani. Dropout as a bayesian approximation: Representing model uncertainty in deep learning. In Maria-Florina Balcan and Kilian Q. Weinberger (eds.), Proceedings of the 33nd International Conference on Machine Learning, ICML 2016, New York City, NY, USA, June 19-24, 2016, volume 48 of JMLR Workshop and Conference Proceedings, pp. 1050-1059. JMLR.org, 2016.
Marta Garnelo, Dan Rosenbaum, Christopher Maddison, Tiago Ramalho, David Saxton, Murray Shanahan, Yee Whye Teh, Danilo Jimenez Rezende, and S. M. Ali Eslami. Conditional neural processes. In Jennifer G. Dy and Andreas Krause (eds.), Proceedings of the 35th International Conference on Machine Learning, ICML 2018, Stockholmsmässon, Stockholm, Sweden, July 10-15, 2018, volune 80 of Proceedings of Machine Learning Research, pp. 1690-1699, PMLR,, 2018.
Anna Gaulton, Louisa J Bellis, A Patricia Bento, Jon Chambers, Mark Davies, Anne Hersey, Yvonne Light, Shaun McGlinchey, David Michalovich, Bissan Al-Lazikani, and John P Overington. ChEMBL: a large-scale bioactivity database for drug discovery. Nucleic Acids Research, 40, 2011.
Pouya M Ghari, Alex Tseng, Gökcen Fraslan, Romain Lopez, Tommaso Biancalani, Gabriele Scalia, and Ehsan Hajiramezanali. Generative flow networks assisted biological sequence editing, In NewrIPS 2023 Generative AI and Biology (GenBio) Workshop, 2023.
Rafael Jömmez-Bombarelli, Jennifer N Wei, David Duvenaud, José Miguel HernándezzLoobto, Benjamín Timothy D Hirzel, Ryan P Adams, and
Sánchez-Lengeling, Dennis Sheberla, Jorge Alán Aspuru-Guzik. Automatic chemical design using a data-driven continuous representation of molecules. ACS Central Science, 4, 2018.
Tan J. Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron C. Courville, and Yoshua Bengio. Generative adversarial nets. In Zoubin Ghahramani, Max Welling, Corinna Cortes, Neil D. Lawrence, and Kilian Q. Weinberger (eds.), Advances in Neural Information Processing Systems 27: Annual Conference on Neural Information Processing Systems 2014, December 8- 13 2014, Montreal, Quebec, Canada, pp. 2672 2680, 2014.
Nate Gruver, Samuel Stanton, Nathan C. Frey, Tim G. J. Rudner, Isidro Hötzel, Julien Lafrance- Vanasse Arvind Rajpal, Kyunghyun Cho, and Andrew Gordon Wilson. Protein design with guided discrete diffusion. In Alice Oh, Tristan Naumann, Amir Globerson, Kate Saenko, Moritz Hardt, and Sergey Levine (eds.), Advances in Neural Information Processing Systems 36: Annual Conference on Neural Information Processing Systems 2023, NeurIPS 2029, New Orleans, LA, USA, December 10 16, 2023, 2023.
Daya Guo, Dejian Yang, Haowei Zhang, Junxiao Song, Poiyi Wang. Qihao Zhu, Runxin Xu, Ruoyu Zhang, Shirong Ma, Xiao Bi, Xiaokang Zhang, Xingkai Yu, Yu Wu, Z. F. Wu, Zhibin Gou, Zhihong Shao, Zhuoshu Li, Ziyi Gao, Aixin Liu, Bing Xue, Bingxuan Wang, Bochao Wu, Bei Feng, Chengda Lu, Chenggang Zhao, Chengqi Deng, Chong Ruan, Damai Dai, Deli Chen, Dongjie Ji, Erhang Li, Fangyun Lin, Fucong Dai, Fuli Luo, Guangbo Hao, Guanting Chen, Guowei Li, H. Zhang, Hanwei Xu, Honghui Ding, Huazuo Gao, Hui Qu, Hui Li, Jianzhong Guo, Jiashi Li, Jingehang Chen, Jingyang Yuan, Jinhao Tu, Junjie Qiu, Junlong Li, J. L. Cai, Jiaqi Ni, Jian Liang, Jin Chen, Kai Dong, Kai Hu, Kaichao You, Kaige Gao, Kang Guan, Kexin Huang, Kuai Yu, Lean Wang, Lecong Zhang, Liang Zhao, Litong Wang, Liyue Zhang, Lei Xu, Leyi Xia, Mingchuan Zhang, Minghua Zhang, Minghui Tang, Mingxu Zhou, Meng Li, Miaojun Wang, Mingming Li, Ning Tian, Panpann Huang, Peng Zhang, Qiancheng Wang, Qinyu Chen, Qiushi Du, Ruiqi Ge,
33

---

Published in Transactions on Machine Learning Research (01/2026)
Ruisong Zhang, Ruizhe Pan, Runji Wang, R. J. Chen, R. L. Jin, Ruyi Chen, Shanghao Lu, Shangyan Zhou, Shanhuang Chen, Shengfeng Ye, Shiyu Wang, Shuiping Yu, Shunfeng Zhou, Shuting Pan, S. S. Ti, Shuang Zhou, Shaoqing Wu, Tao Yun, Tian Pei, Tianyu Sun, T. Wang, Wangding Zeng, Wen Liu, Wenfeng Liang, Wenjun Gao, Wenqin Yu, Wentao Zhang, W. L. Xiao, Wei An, Xiaodong Liu, Xiaohan Wang, Xiaokang Chen, ai Nie, Xin Cheng, Xin Liu, Xin Xie, Xingchao Liu, Xinyu Yang, Xinyuan Li, Xuecheng Su, Xuheng Lin, X. Q Li, Xiangyue Jin, Xiaojin Shen, Xiaosha Chen, Xiaowen Sun, Xiaoxiang Wang, Xinnan Song, Xinyi Zhou, Xianzu Wang, Xinxia Shan, Y. K. Li, Y. Q. Wang, Y. X. Wei, Yang Zhang, Yanhong Xu, Yao Li, Yao Zhao, Yaofeng Sun, Yaohui Wang, Yi Yu, Yichao Zhang, Yifan Shi, Yiliang Xiong, Ying He, Yishi Piao, Yisong Wang, Yixnan Tan, Yiyang Ma, Yiyuan Liu, Yonggiang Guo, Yuan Ou, Yuduan Wang, Yue Gong, Yuheng Zou, Yujia He, Yunfan Xiong, Yuxiang Luo, Yuxiang You, Yuxuan Liu, Yuyang Zhou, Y. X. Zhu, Yanping Huang, Yaohui Li, Yi Zheng, Yuchen Zhu, Yunxian Ma, Ying Tang, Yukun Zha, Yuting Yan, Z. Z. Ren, Zehui Ren, Zhangli Sha, Zhe Fu, Zhean Xu, Zhenda Xie, Zhengyan Zhang, Zhewen Hao, Zhicheng Ma, Zhigang Yan, Zhiyu Wu, Zihui Gu, Zijia Zhu, Zijun Liu, Zilin Li, Ziwei Xie, Ziyang Song, Zizheng Pan, Zhen Huang, Zhipeng Xu, Zhongyu Zhang, and Zhen Zhang. Deepseek-rl incentivizes reasoning in Ilms through reinforcement learning. Nature, 645(8)81)6633 638, 2025.
Tuomas Haarnoja, Aurick Zhou, Kristian Hartikainen, George Tucker, Sehoon Ha, Jie Tan, Vikash Kumar, Henry Zhu, Abhishek Gupta, Picter Abbeel, and Sergey Levine. Soft actor-critic algorithms and applications. arXiv preprinl
2018.
Rishin Haldar and Debajyoti Mukhopadhyay, Levenshtein distance technique in dictionary lookup methods:
An improved approach. arXie preprint arxi 12322 2011.
Kam Hamidich. A data-driven statistical model for predicting the critical temperature of a superconductor. Compulational Materials Science, 154, 2018.
Lars Kai Hansen and Peter Salamon. Neural network ensembles. IEEE Transactions Pattern Analysis and Machine Intelligence, 1990.
James Harrison, John Willes, and Jasper Snoek. Variational bayesian last layers. In The Twelfth International Conference on Learning Representations, ICLR 2024, Vienna, Austria, May 7-11, 2024. OpenReview.ne net, 2024.
Trevor Hastie, Robert Tibshirani, and Jerome Friedman. The Flements of Stalistical Learning: Data Mining, Inference, and Prediction. Springer, 2009.
Geoffrey E Hinton. Training products of experts by minimizing contrastive divergence. Neural Computation, 14, 2002.
Jonathan Ho and Tim Salimans. Classifier-free diffusion guidance. arXiv preprint arXiv:2207.12500 2022.
Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. In Hugo Larochelle, Marc' Aurelio Ranzato, Raia Hadsell, Maria-Florina Balcan, and Hsuan-Tien Lin (eds.), Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, NewrIPS 2020, December 6-12, 2020, virtual, 2020.
Minh Hoang, Azza Fadhel, Aryan Deshwal, Jana Doppa, and Trong Nghia Hoang. Learning surrogates for offline black-box optimization via gradient matching. In Ruslan Salakhutdinov, Zico Kolter, Katherine Heller, Adrian Weller, Nuria Oliver, Jonathan Scarlett, and Felix Berkenkamp (eds.), Proceedings of the 41st International Conference on Machine Learning, volume 235 of Proceedings of Machine Learning Research, pp. 18374-18393, PMLR, 21-27 Jul 2024.
S Hochreiter. Long short-term memory. Neural Computation MIT-Press, 1997.
Chenqing Hua, Yong Liu, Dinghuai Zhang, Odin Zhang, Sitao Luan, Kevin K Yang, Guy Wolf, Doina Precup, and Shuangjia Zheng. Enzymeflow: Generating reaction-specifi enzyme catalytic pockets through flow matching and co-evolutionary dynamics. Xix preprint 2rXiv:2410.0033 2024.
34

---

Published in Transactions on Machine Learning Research (01/2026)
Kexin Huang, Tianfan Fu, Wenhao Gao, Yue Zhao, Yusuf Roohani, Jure Leskovec, Connor W Coley, Cao Xiao, Jimeng Sun, and Marinka Zitnik. Therapeutics data commons: Machine learning datasets and tasks for drug discovery and development. arXie preprint arXiv:2102.095/4 2021.
Evan J. Hughos. Radar waveform optimisation as a many-objoctive application benchmark. In Evoltiionayy Multi-Crie Criterion Oplimization. Spriuger Berlin Heidelberg, 2007.
Hisao Ishibuchi, Naoya Akedo, and Yusuke Nojima. Behavior of multiobjective evolutionary algorithms on many-objective knapsack problems. IEEE Transactions on Evolutionary Computation, 19, 2015.
Himanshu Jain and Kalyanmoy Deb. An evolutionary many-objective optimization algorithm using reference- point based nondominated sorting approach, part ii: Handling constraints and extending to an adaptive approach. IEEE Transactions on Evolutionary Computation, 18, 2014.
Moksh Jain, Emmanuel Bengio, Alex Frrnández-Garrifn Jarrid Rector-Brooks, Bonaventure F. P. Dossou, Chanakya Ajit Ekbote, Jie Fu, Tianyu Zhang, Michael Kilgour, Dinghuai Zhang, Lena Simine, Payel Das, and Yoshua Bengio. Biological sequence design with gllownets. In Kamalika Chaudhuri, Stefanie Jegelka, Le Song, Csaba Szepesvári, Gang Niu, and Sivan Sabato (eds.), International Conference on Machine Learning, TCML 2022, 17-23 July 2022, Baltimore, Maryland, USA, volume 162 of Proceedings of Machine Learning Research, pp. 9786 9801. PMLR, 2022.
Moksh Jain, Sharath Chandra Raparthy, Alex Garnéndez-GGariaa, Jarrid Reclor-Brooks, Yoshua Bengio, Santiago Miret, and Emmanuel Bengio. Multi-objective gflownets. In Andreas Krause, Emma Brunskill, Kyunghyun Cho, Barbara Engelhardt, Sivan Sabato, and Jonathan Scarlett (cds.), International Conference on Machine Learning, ICML 2023, 23-29 July 2023, Honolulu, Hawait, USA, volune 202 of Proceedings of Machine Learning Research, pp. 14631-14653. PMLR, 2023.
Eric Jang, Shixiang Gu, and Ben Poole. Categorical reparameterization with gumbel-softmax. In 5th International Conference on Learning Representations, ICLR 2017, Toulon, France, April 24-26, 2017, Conference Track Proceedings. OpenReview.nel, 2017.
Bowen Jing, Bonnie Berger, and Tommi Jaakkola. AlphaFold meets flow matching for generating protein ensembles. In Ruslan Salakhutdinov, Zico Kolter, Katherine Heller, Adrian Weller, Nuria Oliver, Jonathan Scarlett, and Felix Berkenkamp (eds.), Proceedings of the 41st International Conference on Machine Learning, volume 235 of Proceedinggs of Machine Learning Research, pp. 22277 22303. PMLR, 21 27 Jul 2024.
Donald R Jones, Matthias Schonlau, and William J Welch. Efficient global optimization of expensive black-box functions. Journal of Global Optimization, 13:455 492, 1998.
John Jumper, Richard Evans, Alexander Pritzel, Tim Green, Michael Figurnov, Olaf Ronneberger, Kathryn Tunyasuvuakooo,, Russ Bates, Augustin Zidek, Anna Potapenko, Alex Bridgland, Clemens Meyer, Simon A. A. Kohl, Andrew J. Ballard, Andrew Cowie, Bernardino Romera-Paredes, Stanislav Nikolov, Rishub Jain, Jonas Adler, Trevor Back, Stig Petersen, David Reiman, Ellen Clancy, Michal Zielinski, Martin Steinegger, Michalina Pacholska, Tamas Berghammer, Sebastian Bodenstein, David Silver, Oriol Vinyals, Andrew W. Senior, Koray Kavukcuoglu, Pushmeet Kohli, and Demis Hassabis. Highly accurate protein structure prediction with alphafold. Nature, 596, 2021.
Bhairavi Kannan and S. N. Kramer. An augmented lagrange multiplier based method for mixed integer discrete contimuous optimization and its applications to mechanical design. Journal of Mechanical Design, 116, 1994.
Hyeonah Kim, Minsu Kim, Taeyoung Yun, Sanghyeok Choi, Emmanuel Bengio, Alex Ganddnde--Grricc and Jinkyoo Park. Improved off-policy reinforcement learning in biological sequence design. In NewrIPS 2024 Workshop on AI for New Drug Modalities, 2024a.
Jungtaek Kim. BayesO Benchmarks: Benchmark functions for Bayesian optimization, 2023.
35

---

Published in Transactions on Machine Learning Research (01/2026)
Minsu Kim, Federico Berto, Sungsoo Ahn, and Jinkyoo Park. Bootstrapped training of score-conditioned generator for offline design of biological sequences. In Alice Oh, Tristan Naumann, Amir Globerson, Kate Saenko, Moritz Hardt, and Sergey Levine (eds.), Advances in Neural Information Processing Systems 36: Annual Conference on Neural Information Processing Systems 2023, NeurIPS 2023, New Orleans, LA, USA, December 10 16, 2023, 2023.
Minsu Kim, Joohwan Ko, Tacyoung Yun, Dinghuai Zhang, Ling Pan, Woo Chang Kim, Jinkyoo Park, Emmanuel Bengio, and Yoshua Bengio. Learning to scale logits for temperature-connitionn GFlowNets. In Ruslan Salakhutdinov, Zico Kolter, Katherine Heller, Adrian Weller, Nuria Oliver, Jonathan Scarlett, and Felix Berkenkamp (eds.), Proceedings of the 41st International Conference on Machine Learning, volume 235 of Proceedings of Machine Learning Research, pp. 24248 24270. PMLR. 21-27 Jul 2024b.
Minsu Kim, Taeyoung Yun, Emmanuel Bengio, Dinghuai Zhang, Yoshua Bengio, Sungsoo Ahn, and Jinkyoo Park. Local search gftownets. In The Twelfth International Conference on Learning Representations, ICLR 2024, Vienna, Austria, May 7-11, 2024. OpenRoview.nng net, 2024c.
Diederik P. Kingma and Max Welling. Auto-encoding variational bayes. In Yoshua Bengio and Yann LeCun (cds.), 2nd International Conference on Learning Representations, ICLR 2014, Banff, AB, Canada, April 14-16, 2014, Conference Track Proceedings, 2014.
Andrew Kirjner, Jason Yim, Raman Samusevich, Shahar Bracha, Tommi S. Jaakkola, Regina Barzilay, and Tla R. Fiete. Improving protein optimization with smoothed fitness landscapes. In The Twelfth International Conference on Learning Representations, ICLR 2024, Vienna, Austria, May 7-11, 2024. OpenReview.nug net, 2024.
Justin R Klesmith, John-Paul Bacik, Ryszard Michalczyk, and Timothy A Whitehead. Comprehensive Sequence- Flux mapping of a levoglucosan utilization pathway in e. coli. ACS Synthetic Biology, 4, 2015.
Ivan Kobyzev, Simon JD Prince, and Marcus A Brubaker. Normalizing flows: An introduction and review of current methods. IEEE Transactions on Pattern Analysis and Machine Intelligence, 43, 2020.
Takehisa Kohira, Hiromasa Kemmotsu, Oyama Akira, and Tomoaki Tatsukawa. Proposal of benchmark prob- lem based on real-world car structure design optimization. In Proceedings of the Genelic and Evolutionary Computation Conference Companion, GECCO '18. Association for Computing Machinery, 2018.
Sathvik Kolli. Conflict-averse gradient optimization of ensembles for effective offline model-based optimization. arXiv preprint Xrx:::2303.19934 2023.
Siddarth Krishnamoorthy, Satvik Mehul Mashkaria, and Aditya Grover. Diffusion models for black-box optimization. In Andreas Krause, Emma Brunskill, Kyunghyun Cho, Barbara Engelhardt, Sivan Sabato, and Jonathan Scarlett (eds.), International Conference on Machine Learning, ICML 2023, 23-29 July 2023, Honolulu, Hawaii, USA, volume 202 of Proceedings of Machine Learning Research, pp. PMLR, 2023.
Alex Krizhevsky. Learning multiple layers of features from tiny images, 2009.
Alex Krizhevsky, Ilya Sutskever, and Geoffrey E. Hinton. Imagenet classification with deep convolutional neural networks. In Peter L. Bartlett, Fernando C. N. Pereira, Christopher J. C. Burges, Lóon Bottou, and Kilian Q. Weinberger (eds.), Advances in Neural Information Processing Systems 25: 26th Avnual Conference on Newral Information Processing Systems 2012. Proceedings of a meeling held December 3-6, 2012, Lake Tahoe, Nevada, United States, pp. 1106 1114,111,,,,, 2012.
Jakub Grudzien Kuba, Pieter Abbeel, and Sergey Levine. Cliqueformer: Model-based optimization with structured transformers. arXie preprint arXiv:2410.1311 13106, 2024a.
Kuba Grudzien Kuba, Masatoshi Uehara, Sergey Levine, and Pieter Abbeel. Functional graphical models: Structure enables offline data-driven optimization. In Sanjoy Dasgupta, Stephan Mandt, and Yingzhen Li (eds.), International Conference on Artificial Intelligence and Statistics, 2-4 May 2024, Palou de Congressos, Valencia, Spain, volume 238 of Proceedings of Machine Learning Research, pp. 2449 2457. PMLR, 2024b.
36

---

Published in Transactions on Machine Learning Research (01/2026)
Christopher Kuenneth and Rampi Ramprasad. polybert: a chemical language model to enable fully machine- driven ultrafast polymer informatics. Noture Communicattioss, 14, 2023.
Aviral Kumar and Sergey Levine. Model inversion networks for model-based optimization. In Hugo Larochelle, Marc' Aurelio Ranzato, Raia Hadsell, Maria-Florina Balcan, and Hsuan-Tien Lin (eds.), Advances in Neural Information Processing Systems 33: Annual Conference Neural Information Processing Systems 2020, NewrIPS 2020, December 6-12, 2020, virtual, 2020.
Aviral Kumar, Amir Yazdanbakhsh, Milad Hashemi, Kevin Swersky, and Sergey Levine. Data-driven offline optimization for architecting hardware accelerators. In The Tenth International Conference on Learning Representations, TCLR 2022, Virtual Event, April 25-29, 2022. OpenReview.net, 2022.
Salem Lahlou, Tristan Deleu, Pablo Lemos, Dinghuai Zhang, Alexandra Volokhova, Alex Hernández- Garcia, Léna Néhale Ezzine, Yoshua Bengio, and Nikolay Malkin. A theory of continuous generative flow networks. In Andreas Krause, Emma Brunskill, Kyunghyun Cho, Barbara Engelhardt, Sivan Sabato, and Jonathan Scarlett (eds.), International Conference on Machine Learning, ICML 2023, 23-29 July 2023, Honolulu, PMLR, 2023a.
Hawaii, USA, volume 202 of Proceedings of Machine Learning Research, pp-
Salem Lahlou, Moksh Jain, Hadi Nekoei, Victor Butoi, Paul Bertin, Jarrid Rector-Brooke Maksym Korablyov, and Yoshua Bengio. DEUP: Direct epistemic uncertainty prediction. Transactions on Machine Learning Research, 2023b.
Balaji Lakshminarayanan, Alexander Pritzel, and Charles Blundell. Simple and scalable predictive uncertainty estimation using deep ensembles. In Isabelle Guyon, Ulrike von Luxburg, Samy Bengio, Hanna M. Wallach, Rob Fergus, S. V. N. Vishwanathan, and Roman Garnett (eds.), Advances in Neural Information Processing Systems 30: Annual Conference on Neural Information Processing Systems 2017, December 4-9, 2017, Long Beach, CA, USA, pp. 6402-6413, 2017.
J. Lampinen and Ivan Zelinka. Mixed intego-ddisneee-cootinooss optimization by differential evolution part 2: a practical example, 2000.
Matthew Le, Apoorv Vyas, Bowen Shi, Brian Karrer, Leda Sari, Rashel Moritz, Mary Williamson, Vimal Manohar, Yossi Adi, Jay Mahadeokar, and Wei-Ning Hsu. Voicebox: Text-guided multilingual universal speech generation at scale. In Alice Oh, Tristan Naumann, Amir Globerson, Kate Saenko, Moritz Hardt, and Sergey Levine (eds.), Advances in Neural Information Processing Systems 36: Annual Conference on Neural Information Processing Systems 2023, NewrIPS 2023, New Orleans, LA, USA, December 10 16, 2023, 2023.
Yann LeCun, Sumit Chopra, Raia Hadsell, Aurelio Ranzato, and Fu Jie Huang. A tutorial on energy-based learning. Predicting Structured Data 1, 2006.
Yann LeCun, Yoshua Bengio, and Geoffrey Hinton. Deep learning. Nature, 521((5533::366 444, 2015.
Seul Lee, Jachyeong Jo, and Sung Ju Hwang. Exploring chemical space with score-based out-of-dian distribution generation. In Andreas Krause, Emma Brunskill, Kyunghyun Cho, Barbara Engelhardt, Sivan Sabato, and Jonathan Scarlett (eds.), International Conference on Machine Learning, ICML 2023, 23-29 July 2023, Honolulu, Hawaii, USA, volume 202 of Proceedings of Machine Learving Research, pp. 18872 18892. PMLR, 2023.
Seunghun Lee, Jinyoung Park, Jaewon Chu, Minseo Yoon, and Hyunwoo J. Kim. Latent bayesian opti- mization via autoregressive normalizing flows. In The Thirteenth International Conference on Learning Representations, ICLR 2025, Singapore, April 24-28, 2025. OpenReview.net, 2025.
Sergey Levine, Aviral Kumar, George Tucker, and Justin Fu. Offline reinforcement learning: Tutorial, review, and perspectives on open problems. arXiv preprint arXa::205.001 01 643, 2020.
Xingtao Liao, Qing Li, Xujing Yang, Weigang Zhang, and Wei Li. Multiobjective optimization for crash safety design of vehicles using stepwise regression model. Structural and Multidisciplinary Optimization, 35, 2008.
37

---

Published in Transactions on Machine Learning Research (01/2026)
Yaron Lipman, Ricky T. Q Chen, Heli Ben- Ben-Hamm, Maximilian Nickel, and Matthew Le. Flow matching for generative modeling. In The Fleventh International Conference on Learning Represenlations, TCL. 2023, Kigali, Rwanda, May 1-5, 2023. OpenReview.ner net, 2023.
Dianbo Liu, Moksh Jain, uonaventure F. P. Dossou, Qianli Shen, Salem Lahlou, Anirudh Goyal, Nikolay Malkin, Chris Chinenye Emeeue, Dinghuai Zhang, Nadhir Hassen, Xu Ji, Kenji Kawaguchi, and Yoshua Bengio. Gflowout: Dropout with generative flow networks. In Andreas Krause, Emma Brunskill, Kyunghyun Cho, Barbara Engelhardt, Sivan Sabato, and Jonathan Scarlett (eds.), International Conference on Machine Learning, ICML 2023, 23-29 July 2023, Honobulu, Hawaii, USA, volume 202 of Proceedings of Machine Learning Research, pp. 21715 21729. PMTR, 2023.
Hanxiao Liu, Karen Simonyan, and Yiming Yang. DARTS: differentiable architecture search. In 7th International Conference on Learning Representations, 1CLR 2019, New Orleans, LA, USA, May 6-9, 2019. OpenReview.net, 2019.
Jeremiah Z. Liu, Zi Lin, Shreyas Padhy, Dustin Tran, Tania Bedrax-Weiss, and Balaji Lakshminarayanan. Simple and principled uncertainty estimation with deterministic deep learning via distance awareness. In Hugo Larochelle, Marc' Aurelio Ranzato, Raia Hadsell, Maria-Florina Balcan, and Hsuan-Tien Lin (eds.), Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020, NewrIPS 2020, December 6-12, 2020, virtual, 2020.
Qiang Liu and Dilin Wang. Stein variational gradient descent: general purpose bayesian inference algorithm. In Daniel D. Lee, Masashi Sugiyama, Ulrike von Luxburg, Isabelle Guyon, and Roman Garnett (eds.), Advances in Newrol Information Processing Systems 29: Annual Conference on Neural Information Processing Systems 2016, December 5-10 5-10, 2016, Barcelona, Spain, pp.
2016.
Ronny Lorenz, Stephan H. Bernhart, Christian Höner zu Siederdissen, Hakim Tafer, Christoph Flamm, Peter F. Stadler, and Ivo L. Hofacker. Viennarna package 2.0. Algorithms for Molecular Biology, 6, 2011.
Zhichao Lu, Ran Cheng, Yaochu Jin, Kay Chen Tan, and Kalyanmoy Deb. Neural architecture search as multiobjective optimization benchmarks: Problem formulation and performance assessment. IEEE Transactions on Fuobutionary Compulation, 2023.
Renqian Luo, Fei Tian, Tao Qin, Enhong Chen, and TieYYan Liu. Neural architecture optimization. In Samy Bengio, Hanna M. Wallach, Hugo Larochelle, Kristen Grauman, Nicolò Cosa-Bianchi, and Roman Garnett (eds.), Advances in Newral Information Processing Systems 31: Annual Conference on Neural Information Processing Systems 2018, NewrIPS 2018, December 3-8, 2018, Montréal, Canada, pp. -837, 2018.
Shitong Luo, Yufeng Su, Xingang Peng, Sheng Wang, Jian Peng, and Jianzhu Ma. Antigen-specific antibody design and optimization with diffusion-baass based generative models for protein structures. In Sanmi Koyejo, S. Mohamed, A. Agarwal, Danielle Belgrave, K. Cho, and A. Oh (eds.), Advances in Neural Information Processing Systems 35: Annual Conference on Newral Information Processing Systems 2022, NeurIPS 2022, New Orleans, LA, USA, November 28- December 9, 2022, 2022.
Thibaut Lust and Jacques Teghem. The multiobjective traveling salesman problem: A survey and a new approach. In Advances in Mulli- Objective Nature Inspired Compuling. Springer, 2010.
Xiaoliang Ma, Yanan Yu, Xiaodong Li, Yutao Qi, and Zexuan Zhu. survey of weight vector adjust- ment methods for decomposition-bassed multiobjective evolutionary algorithms. IEFF Transactions Evolutionary Computation, 2020.
Kanika Madan, Jarrid Rector-Brooke Maksym Korablyov, Emmanuel Bengio, Moksh Jain, Andrei Cristian Nica, Tom Bose, Yoshua Bengio, and Nikolay Malkin. Learning gllownets from partial episodes for improved convergence and stability. In Andreas Krause, Emma Brunskill, Kyunghyun Cho, Barbara Engelhardt, Sivan Sabato, and Jonathan Scarlett (ods.), International Conference on Machine Learning, TCML 2023, 23-29 July 2023, Honolulu, Hawaii, USA, volume 202 of Proceedings of Machine Learning Research, pp. 13467-23488 PMTRR 2023.
38

---

Published in Transactions on Machine Learning Research (01/2026)
Nikolay Malkin, Moksh Jain, Emmanuel Bengio, Chen Sun, and Yoshua Bengio. Trajectory balance: Improved credit assignment in gflownets. In Sanmi Koyejo, S. Mohamed, A. Agarwal, Danielle Belgrave, K. Cho, and A. Oh (eds.), Advonces in Neural Information Processing Systems 35: Annual Conference on Neural Information Processing Systems 2022, NeurIPS 2022, New Orleans, LA, USA, November 28- - December 9, 2022, 2022.
Nikolay Malkin, Salem Lahlou, Tristan Delcu, Xu Ji, Edward J. Hu, Katie Everett, Dinghuai Zhang, and Yoshua Bengio. Gflownets and variational inference. In The Fleventh International Conference on Learning Representations, ICLR 2023, Kigali, Rwanda, May 1-5, 2023. OpenReview net, 2023.
Satvik Mehul Mashkaria, Siddarth Krishnamoorthy, and Aditya Grover. Generative pretraining for black-box optimization. In Andreas Krause, Emma Brunskill, Kyunghyun Cho, Barbara Engelbardt, Sivan Sabato, and Jonathan Scarlett (eds.), International Conference on Machine Learning, ICML 2023, 28-29 July 2023, Honolulu, Hawait, USA, volume 202 of Proceedings of Machine Learning Research, pp. PMLR, 2023.
Daniel Melamed, David I, Young, Caitlin E Gamble, Christina R Miller, and Stanley Fields. Deep mutational scanning of an RRM domain of the saccharomyces cerevisiae poly(a)-binding protein. RNA, 19, 2013.
Alexander Mordvintsev, Christopher Olah, and Mike Tyka. Inceptionism: Going deeper into neural networks, 2015.
Radford M Neal. Probabilistic inference using markov chain monte carlo methods, 1993.
Tung Nguyen, Sudhanshu Agrawal, and Aditya Grover. Expt: Synthetic pretraining for few-shot experimental design. In Alice Oh, Tristan Naumann, Amir Globerson, Kate Sacnko, Moritz Hardt, and Sorgey Levine (eds.), Advances in Newral Information Processing Systems 36: Annual Conference on Neural Information Processing Systems 2023, NewrlPS 2023, New Orleans, LA, USA, December 10 16, 2023, 2023.
Pierce J. Ogden, Eric D. Kelsic, Sam Sinai, and George M. Church. Comprehensive aav capsid fitness landscape reveals a viral gene and enables machine-guided design. Science, 366, 2019.
Long Ouyang, Jeffrey Wu, Xu Jiang, Diogo Almeida, Carroll L. Wainwright, Pamela Mishkin, Chong Zhang, Sandhini Agarwal, Katarina Slama, Alex Ray, John Schulman, Jacob Hilton, Fraser Kelton, Luke Miller, Maddie Simens, Amanda Askell, Peter Welinder, Paul F. Christiano, Jan Leike, and Ryan Lowe. Training language models to follow instructions with human feedback. In Sanmi Koyejo, S. Mohamed, A. Agarwal, Danielle Belgrave, K. Cho, and A. Oh (eds.), Advances in Neurol Information Processing Systems 35: Annual Conference on Neural Information Processing Systems 2022, NewrIPS 2022, New Orleans, LA, USA, November 28- December 9, 2022, 2022.
Michael Parsons and Randall Scott. Formulation of multicriterion design optimization problems for solution with scalar numerical optimization methods. Journal of Ship Research, 48, 2004.
Rafael Figueiredo Prudencio, Marcos ROA Maximo, and Esther Luna Colombini. A survey on offline reinforcement learning: Taxonomy, review, and open problems. IEFE Transactions on Neural Networks and Learning Systems, 2023.
Han Qi, Yi Su, Aviral Kumar, and Sergey Levine. Data-driven offline decision-making via invariant repre- sentation learning. In Sanmi Koyejo, S. Mohamed, A. Agarwal, Danielle Belgrave, K. Cho, and A. Oh (eds.), Advances in Newral Information Processing Systems 35: Annual Conference on Neural Information Processing Systems 2022, NewrIPS 2022, New Orleans, LA, USA, November 28- December 9, 2022, 2022.
Han Qi, Xinyang Geng, Stefano Rando, Iku Ohama, Aviral Kumar, and Sergey Levine. Latent conservative objective models for data-driven crystal structure prediction. arXiv preprint wrXiw:2310010008 2023.
Hong Qian, Yiyi Zhu, Xiang Shu, Xin An, Yaolin Wen, Shuo Liu, Huakang Lu, Aimin Zhou, Ke Tang, and Yang Yu. S00-bench: Benchmarks for evaluating the stability of offiine black-box optimization. In The Thirteenth International Conference on Learning Representations, ICLR 2025, Singapore, April 24-28, 2025. OpenReview.neg, 2025.
39

---

Published in Transactions on Machine Learning Research (01/2026)
Carl Edward Rasmussen and Christopher K. I. Williams. Gaussian Processes for Machine Learning. MIT Press, 2006.
Tapabrata Ray and K. Liew. Liew, k. A swarm metaphor for multiobjective design optimization. engineering optimization 34, 141-153. Engineering Optimization, 34, 2002.
Tapabrata Ray, K. Tai, and KIN SEOW. Multiobjective design optimization by an evolutionary algorithm. Engineering Optimization, 33, 2001.
Zhizhou Ren, Jiahan Li, Fan Ding, Yuan Zhou, Jianzhu Ma, and Jian Peng. Proximal exploration for model- guided protein sequence design. In Kamalika Chaudhuri, Stefanic Jegelka, Le Song, Csaba Szepesvári, Gang Niu, and Sivan Sabato (eds.), International Conference on Machine Learning, ICML 2022, 17-23 July 2022, Baltimore, Maryland, USA, volume 162 of Proceedings of Machine Learning Research, pp. 18520 18536. PMLR, 2022.
Sebastian Ruder. An overview of gradient descent optimization algorithms. arXiv preprint Xr 100..04477 2016.
Paul J Sample, Ban Wang, David W Reid, Vlad Prosnyak, lain J McFadyen, David R Morris, and Georg Seelig. Human 5 utr design and variant effect prediction from massively parallel translation assay. Noture Biolechnology, 2019.
Karen S. Sarkisyan, Dmitry A. Bolotin, Margarita V. Meer, Dinara R. Usmanova, Alexander S. Mishin, George V. Sharonov, Dmitry N. Ivankov, Nina G. Bozhanova, Mikhail S. Baranov, Onuralp Soylemez, Natalya S. Bogatyreva, Peter K. Vlasov, Evgeny S. Egorov, Maria D. Logacheva, Alexey S. Kondrashov, Dmiiry M. Chudakov, Ekaterina V. Putintseva, Nlgar Z. Mamedov, Dan S. Tawfik, Konstantin A. Lukyanov, and Fyodor A. Kondrashov. Local fitness landscape of the green fluorescent protein. Nature, 533, 2016.
Joost Schymkowitz, Jesper Borg, Francois Stricher, Robby Nys, Frederic Rousseau, and Luis Serrano. The foldx web server: an online force field. Nucleic Acids Research, 33, 2005.
Joar Skalse, Nikolaus H. R. Howe, Dmitrii Krasheninnikov, and David Krueger. Defining and characterizing reward gaming. In Sanmi Koyejo, S. Mohamed, A. Agarwal, Daniclle Belgrave, K. Cho, and A. Oh (eds.), Advances in Neurol Information Processing Systems 35: Annual Conference on Neural Information Processing Systems 2022, NewrIPS 2022, New Orleans, LA, USA, November 28- December 9, 2022, 2022.
Xingyou Song, Oscar Li, Chansoo Lee, Bangding Yang, Daiyi Peng, Sagi Perel, and Yutian Chen. Omnipred: Language models as universal regressors. Trensactions on Machine Learning Research, 2024.
Samuel Stanton, Wesley J. Maddox, Nate Gruver, Phillip Maffettone, Emily Delaney, Peyton Greenside, and Andrew Gordon Wilson. Accelerating bayesian optimization for biological sequence design with denoising autoencoders. In Kamalika Chaudhuri, Stefanie Jegelka, Le Song, Csaba Szepesvári, Gang Niu, and Sivan Sabato (eds.), International Conference on Machine Learning, ICML. 2022, 17-23 July 2022, Baltimore, Moryland, USA, volume 162 of Proceedings of Machine Learning Research, pp. 20450 20478. PMLR, 2022.
Samuel Stanton, Robert Alberstein, Nathan Frey, Andrew Watkins, and Kyunghyun Cho. Closed-form test functions for biophysical sequence optimization algorithms. In (CML'24 Workshop ML for Life and Material Science: From Theory to Industry Applications, 2024.
Lea. M. Starita, Jonathan N. Pruneda, Russell S. Lo, Douglas M. Fowler, Helen J. Kim, Joseph B. Hiatt, Jay Shendure, Peter S. Brzovic, Stanley Fields, and Rachel E. Klevit. Activity-enhancing mutations in an c3 ubiquitin ligase identified by high-throughput mutagenesis. Proceedings of the National Academy of Sciences, 110, 2013.
Hannes Stärk, Bowen Jing, Chenyu Wang, Gabriele Corso, Bonnie Berger, Regina. Barzilay, and Tommi S. Jaakkola. Dirichlet flow matching with applications to DNA sequence design. In Forty-first International Conference on Machine Learning, ICML 2024, Vienma, Austria, July 21-27, 2024. OpenReview.nes, 2024.
S. Surjanovic and D. Bingham. Virtual library of simulation experiments: Test functions and datasets, 2013.
40

---

Published in Transactions on Machine Learning Research (01/2026)
Richard S Sutton and Andrew G Barto. Reinforcement learning: An introduction, volume 1. MIT press Cambridge, 1998.
Rong-Xi Tan, Ke Xue, Shen-Huan Lyu, Haopu Shang, yaowang, Yaoyuan Wang, Fu Sheng, and Chao Qian. Offiin model-based optimization by learning to rank. In The Thirteenth International Conference on Learning Representations, ICLR 2025, Singapore, April 24-28, 2025. OpenReview.ne net, 2025.
Ryoji Tanabe and Hisao Ishibuchi. An cosy-lo-use real-world multi-objective optimization problem suite. Applied Soft Computing, 89, 2020.
Tijmen Tieleman. Training restricted boltzmann machines using approxinations to the likelihood gradient. In William W. Cohen, Andrew McCallum, and Sam T. Roweis (eds.), Machine Learning, Proceedings of the Tweenty-Fift International Conference (ICML 2008), Helsinki, Finland, June 5-9, 2008, volume 307 of ACM International Conference Proceeding Series, pp. 1064 1071. ACM, 2008. doi: 10.1145/ 1190116..0111000000
Emanuel Todorov, Tom Erez, and Yuval Tassa. Mujoco: A physics engine for model- control. In 2012 (EEE/RSJ International Conference Intelligent Robots and Systems, 2012.
Brandon Trabucco, Aviral Kumar, Xinyang Geng, and Sergey Levine. Conservative objective models for effective offiine model-based optimization. In Marina Mcila and Tong Zhang (eds.), Proceedings of the 38th International Conference on Machine Learning, ICML 2021, 18-24 July 2021, Virtual Evenl, volume 139 of Proceedings of Machine Learning Research, pp. 10358 10368, PMLR, 2021.
Brandon Trabucco, Xinyang Geng, Aviral Kumar, and Sergey Levine. Design- bench: Benchmarks for data-driven offline model-based optimization. In Kamalika Chaudhuri, Stefanie Jegelka, Te Song, Csaba Szepesvári, Gang Niu, and Sivan Sabato (eds.), International Conference on Machine Learning, JCML 2022, 17-23 July 2022, Baltimore, Maryland, USA, volume 162 of Proceedings of Machine Learning Research, pp- 21658 21676. PMLR, 2022.
Rajkumar Vaidyanathan, Kevin Tucker, Nilay Papila, and Wei Shyy. Cid-based design optimization for single element rocket injector. NASA Technical Reports Server, 2003.
Homero Valladares, Tianyi Li, Likun Zhu, Hazim El-Mounayri, A.M.A. Hashem, Ashraf Abdel-Ghany, and Andres Tovar. Bayesian optimization of active materials for lithium-ion batteries. In Proceedings of The 47th Annual Conference of the IEEE Industrial Electronics Society, 2021.
David A. van Veldhuizen and Gary B. Lamont. Multiobjective evolutionary algorithm test suites. In Proceedings of the 1999 ACM Symposium on Applicd Computing, Sac '99. Association for Computing Machinery, 1999.
Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N. Gomez, Lukasz Kaiser, and Illia Polosukhin. Attention is all you need. In Isabelle Guyon, Ulrike von Luxburg, Samy Bengio, Hanna M. Wallach, Rob Fergus, S. V. N. Vishwanathan, and Roman Garnett (eds.), Advances in Neural Information Processing Systems 30: Annual Conference on Neural Information Processing Systems 2017, December 4-9, 2017, Long Beach, CA, USA, pp. 5998 6008, 2017.
Vanessa Volz, Boris Naujoks, Pascal Kerschke, and Tea Tušar. Single- and multi-objectivve came-benchman for cvolutionary algorithms. In Proceedings of the Genetic and Evolutionary Computation Conference, GECCO '19. Association for Computing Machinery, 2019.
Xinyou Wang, Zaixiang Zheng, Fei Ye, Dongyu Xue, Shujian Huang, and Quanquan Gu. Diffusion language models are versatile protein learners. In Ruslan Salakhutdinov, Zico Kolter, Katherine Heller, Adrian Weller, Nuria Oliver, Jonathan Scarlett, and Felix Berkenkamp (eds.), Proceedings of the 41st International Conference on Machine Learning, volume 235 of Proceedings of Machine Learning Research, pp. PMLR, 21 27 Jul 2024.
Zichen Wang, Steven A. Combs, Ryan Brand, Miguel Romero Calvo, Panpan Xu, George Price, Nataliya Golovach, Emmanuel O. Salawu, Colby J. Wisc, Sri Priya Ponnapalli, and Peter M. Clark. Lmngvp: an extensible sequence and structure informed deep learning framework for protein property prediction. Scientific Reports, 12, 2022.
41

---

Published in Transactions on Machine Learning Research (01/2026)
Joseph L. Watson, David Juergens, Nathaniel R. Bennett, Brian L. Trippe, Jason Yim, Helen E. Eisenach, Woody Ahern, Andrew J. Borst. Robert J. Ragotte, Lukas F. Milles, Basile I. M. Wieky, Nikita Hanikel, Samuel J. Pellock, Alexis Courbet, William Sheffler, Jue Wang, Preetham Venkatesh, Isaac Sappington, Susana Vázquez Torres, Anna Lauko, Valentin De Bortoli, Emile Mathicu, Sergey Ovchinnikov, Regina Barzilay, Tommi S. Jaakkola, Frank DiMaio, Minkyung Back, and David Baker. De novo design of protein structure and function with rfdiffusion. Nature, 620, 2023.
Jochen Weile, Song Sun, Atina G Cote, Jennifer Knapp, Marta Verby, Joseph C Mellor, Yingzhou Wu, Carles Pons, Cassandra. Wong, Natascha van Licshout, Fan Yang, Murat Tasan, Guihong Tan, Shan Yang, Douglas M Fowler, Robert Nussbaum, Jesse D Bloom, Mare Vidal, David Hill, Patrick Aloy, and Frederick P Roth. framework for exhaustively mapping functional missense variants. Molecular Systems Biology, 13, 2017.
Christopher Williams and Carl Rasmussen. Gaussian processes for regression. In D. Touretzky, M.C. Mozer, and M. Hasselmo (eds.), Advances in Neural Information Processing Systems 8: Annual Conference on Newral Information Processing Systems 1995, NewrIPS 1995, Denver, Colorado, USA, November 27- December 2, 1995, volume 8. MIT Press, 1995.
Andrew Gordon Wilson, Zhiting Hu, Ruslan Salakhutdinov, and Fric P. Xing. Deep kernel learning. In Arthur Gretton and Christian C. Robert (ods.), Proceedings of the 19th International Conference on Artificial Intelligence and Statistics, AISTATS 2016, Cadiz, Spain, May 9-11, 2016, volume 51 of JMLR Workshop and Conference Proceedings, pp. 370-30 370-378. JMLR.org. 2016.
Emily E Wrenbeck, Laura R Azouz, and Timothy A Whitehead. Single-mutation fitness landscapes for an enzyme on multiple substrates reveal specificity is globally encoded. Nature Communications, 8, 2017.
Jie Xu, Yunsheng Tian, Pingchuan Ma, Daniela Rus, Shinjiro Sueda, and Wojeiech Matusik. Prediction multi-objective reinforcement learning for contimuous robot control. In Proceedings of the 37th International Conference on Machine Learning, ICML 2020, 19-18 July 2020, Virtual Event, volume 119 of Proceedings of Machine Learning Research, pp. 10607-10614 PMLR, 2020.
Minghao Xu, Zuobai Zhang, Jiarui Lu, Zhaocheng Zhu, Yangtian Zhang, Chang Ma, Runcheng Liu, and Jian Tang. PEER: A comprehensive and multi-task benchmark for protein sequence understanding. In Sanmi Koyejo, S. Mohamed, A. Agarwal, Danielle Belgrave, K. Cho, and A. Oh (eds.), Advances in Neural Information Processing Systems 35: Annual Conference on Neural Information Processing Systems 2022, NewrIPS 2022, New Orleans, LA, USA, November 28- December 9, 2022, 2022.
Ke Xue, Rongxi Tan, Xiaobin Huang, and Chao Qian. Offline multi-objective optimization. In Ruslan Salakhutdinov, Zico Kolter, Katherine Heller, Adrian Weller, Nuria Oliver, Jonathan Scarlett, and Felix Berkenkamp (eds.), Proceedings of the 41st International Conference on Machine Learning, volume 235 of Proceedings of Machine Learning Research, pp. 55595-55622 PMLR, 21-27 Jul 2024.
Chengrun Yang, Xuezhi Wang, Yifeng Lu, Hanxiao Liu, Quoe V. Le, Denny Zhou, and Xinyun Chen. Large language models as optimizers. In The Twelfth International Conference on Learning Representations, ICLR 2024, Vienno, Austria, May 7-11, 2024. OpenReview.net, 2024.
Kevin K Yang, Zachary Wu, and Frances H Arnold. Machine-learning guided directed evolution for protein engincering. Nature Methods, 1688)6687-694 2019.
Michael S. Yao, Yimeng Zeng, Hamsa Bastani, Jacob R. Gardner, James C. Gee, and Osbert Bastani. Generative adversarial model-based optimization via source critic regularization. In Amir Globersons, Lester Mackey, Danielle Belgrave, Angela Fan, Ulrich Paquet, Jakub M. Tomczak, and Cheng Zhang (eds.), Advances in Neural Information Processing Systems 38: Annual Conference on Neural Information Processing Systems 2024, NeurIPS 2024, Vancouver, BC, Canada, December 10 15, 2024, 2024a.
Michael Yao, James C Gee, and Osbert Bastani. Diversity by design: Leveraging distribution matching for offline model-based optimization. In International Conference on Machine Learning, ICML 2025, 18-19 July 2025, Vancouser, BC, Canada, Proceedings of Machine Learning Research. PMLR, 2025.
42

---

Published in Transactions on Machine Learning Research (01/2026)
Yinghua Yao, Yuangang Pan, Jing Li, Ivor Tsang, and Xin Yao. Proud: Pareto-guided diffusion model for multi-objective generation. Machine Learning, 2024b.
Fei YE, Zaixiang Zheng, Dongyu Xue, Yuning Shen, Lihao Wang, Viming Ma, Yan Wang, Xinyou Wang, Xiangxin Zhou, and Quanquan Gu. Proteinbench: holistic evaluation protein foundation models. In The Thirleenth International Conference on Learning Representations, ICLR 2025, Singapore, April 24-28, 2025. OpenReview.nn net, 2025.
Peiyu Yu, Dinghuai Zhang, Hengzhi He, Xiaojian Ma, Ruiyao Miao, Yifan Lu, Yasi Zhang, Deqian Kong, Ruiqi Gao, Jianwen Xie, Guang Cheng, and Ying Nian Wu. Latent energy-based odyssey; Black-box optimization via expanded exploration in the energy-based latent space. arXiv preprint arXiv:445.116300 2024.
Sihyun Yu, Sungsoo Ahn, Te Song, and Jinwoo Shin. Roma: Robust model adaptation for offline model- basod optimization. In Marc' Aurclio Ranzato, Alina Beygelzimer, Yann N. Dauphin, Percy Liang, and Jennifer Wortman Vaughan (eds.), Advances in Neural Information Processing Systems 34: Annual Conference on Neurol Information Processing Systems 2021, NeurIPS 2021, December 6- 14, 2021, virtual, pp. 4619-4631, 2021a.
Tianhe Yu, Saurabh Kumar, Abhishek Gupta, Sergey Levine, Karol Hausman, and Chelsea Finm. Gradient surgery for multi-task learning. In Hugo Larochelle, Marc'Aurelis Ranzato, Raia Hadsell, Maria-Florina Balcan, and Hsuan-Tiee Tin (eds.), Advances in Neurul Information Processing Systems 39: Annual Conference on Neurol Information Processing Systems 2020, NeurIPS 2020, December 6-12, 2020, virtual, 2020.
Tianhe Yu, Aviral Kumar, Rafael Rafailov, Aravind Rajeswaran, Sergey Levine, and Chelsea Finn. COMBO: conservative offiine model-based policy optimization. In Mare' Aurelio Ranzato, Alina Beygelzimer, Yann N. Dauphin, Percy Liang, and Jennifer Wortman Vaughan (eds.), Advances in Neural Information Processing Systems 94: Annual Conference on Neural Information Processing Systems 2021, NeurIPS 2021, December 6-14, 2021, virtual, pp. 28954 28954-28967, 2021b.
Ye Yuan, Can Chen, Zixuan Liu, Willie Neiswanger, and Xue (Steve) Liu. Importance-aware co-teaching for offline model-based optimization. In Alice Oh, Tristan Naumann, Amir Globerson, Kate Sacnko, Moritz Hardt, and Sergey Levine (eds.), Advances in Neural Information Processing Systems 36: Annual Conference on Neural Information Processing Systems 2023, NewrIPS 2023, New Orleans, LA, USA, December 10 16, 2023, 2023.
Ye Yuan, Youyuan Zhang, Can Chen, Haolun Wu, Zixuan Li, Jianmo Li, James J. Clark, and Xue Liu. Design editing for offline model-basee optimization. Transactions on Machine Learning Research, 2024.
Ye Yuan, Can Chen, Christopher Pal, and Xue Liu. Parctoflow: Guided flows in multi-objective optimization. In The Thirteenth International Conference Learning Representations, ICLR 2025, Singapore, April 24-28, 2025. OpenReview.net: 2025.
Tacyoung Yun, Sujin Yun, Jacwoo Loe, and Jinkyoo Park. Guided trajectory generation with diffusion models for offline model-based optimization. Amir Globersons, Lester Mackey, Danielle Belgrave, Angela Fan, Ulrich Paquet, Jakub M. Tomezak, and Cheng Zhang (eds.), Advances Neural Information Processing Systems 38: Annual Conference on Neural Information Processing Systems 2024, NewrIPS 2024, Vancouver, BC, Canada, December 10- 15, 2024, 2024.
Taeyoung Yun, Kiyoung Om, Jaewoo Lee, Sujin Yun, and Jinkyoo Park. Posterior inference with diffusson models for bigh-dimenssooal black-box optimization. In International Conference on Machine Learning, ICML 2025, 19-19 July 2025, Vancouver, BC, Canada, Proccedings of Machine Learning Research. PMLR, 2025.
Sandra Zajac and Sandra Huber. Objectives and methods in multi-objective routing problems: a survey and classification scheme. European Journal of Operational Research, 290, 2021.
43

---

Published in Transactions on Machine Learning Research (01/2026)
Dinghuai Zhang, Nikolay Malkin, Zhen Liu, Alexandra Volokhova, Aaron C. Courville, and Yoshua Bengio. Generative flow networks for discrete probabilistic modeling. In Kamalika Chaudhuri, Stefanie Jegelka, Le Song, Csaba Szepesvári, Gang Niu, and Sivan Sabato (eds.), International Conference on Machine Learning, ICML 2022, 17-28 July 2022, Baltimore, Maryland, USA, volume 162 Proceedings of Machine Learning Research, pp. 26412 26428. PMLR, 2022.
Qiang Zhang, Ruida Zhou, Yang Shen, and Tie Liu. From lunction to distribution modeling: A PAC-generalive approach to offline optimization. In NeurlPS 2024 Workshop on Data-driven and Differentiable Simulations, Surrogates, and Solvers, 2024.
Zuobai Zhang, Chuanrui Wang, Minghao Xu, Vijil Chenthamarakshan, Aurélie Lozano, Payel Das, and Jian Tang, A systematic study of joint representation learning on protein sequences and structures, arXiv preprint 1.Xi::2303.06277 2023.
Yiyang Zhao, Linnan Wang, Kevin Yang, Tianjun Zhang, Tian Guo, and Yuandong Tian. Multi-objective op- timization by learning space partition. In The Tenth International Conference Learning Representations, ICLR 2022, Virtual Event, April 25-29, 2022. Openleeview.net, 2022.
Qinqing Zheng, Matt Le, Neta Shaul, Yaron Lipman, Aditya Grover, and Ricky TQ Chen. Guided flows for generative modeling and decision making. arXiv preprint arXic:2311.13443, 2023.
E Zitzler, K Deb, and L Thiele. Comparison of multiobjectivee evolutionary algorithms: empirical results. Evol Comput, 8, 2000.
Eckart Zitzler and Lothar Thiele. Multiobjective optimization using evolutionary algorithms comparative case study. In Parallel Problem Solving from Nature PPSN V. Springer Berlin Heidelberg, 1998.
Barret Zoph and Quoe V. Le. Neural architecture search with reinforcement learning. In 5th International Conference on Learning Representations, ICLR 2017, Toulon, France, April 24-26, 2017, Conference Track Proceedings. OpenReview.nee net, 2017.
44


Reviews:
[{"review_id": "5del1kcRmz", "reviewer": "Reviewer_C3xe", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper presents a comprehensive review of offline model based optimization (MBO), an emerging field that combines surrogate modeling and generative modeling to address black box optimization using fixed offline datasets.\nIt formalizes both single objective and multi objective settings, categorizes benchmark tasks (synthetic, real world, scientific, and machine learning model), and surveys recent methodological advances.\nThe paper also highlights open challenges such as uncertainty estimation, realistic benchmarking, and causal graphical modeling.\n\nStrengths\n* First systematic synthesis of the offline MBO literature, bridging surrogate and generative perspectives.\n* Clear taxonomy and well structured exposition that serves both newcomers and experts.\n* Broad coverage across diverse application domains including protein design, material discovery, and neural architecture search.\n\nWeaknesses\n* Very broad scope, sometimes at the cost of depth; some methods are summarized descriptively rather than critically.\n* Empirical comparison and reproducibility standards are not extensively discussed.\n* Sections on AI safety and LLM alignment are speculative and should either be grounded in examples or clearly marked as forward looking commentary.", "claims_and_evidence_yn": "Yes", "claims_explanation": "Mostly yes. The claims about taxonomy, challenges, and observed trends are well supported by the cited literature. The arguments are logically consistent and clearly written.\nHowever, some statements in the future direction sections (for example causal modeling and LLM alignment) are aspirational rather than evidence based. Providing concrete references or illustrative examples would make those arguments stronger.", "audience_yn": "Yes", "audience_explanation": "The topic fits well within TMLR’s audience because it connects several subfields of modern machine learning.\nThe writing is pedagogical while remaining technically sound, making it accessible to a broad readership.\nGiven the field’s rapid growth and the lack of comparable surveys, this paper would be valuable to both theoretical and applied researchers.", "requested_changes": "* (Minor) Add a comparative table contrasting surrogate and generative modeling approaches along axes such as data dependence, uncertainty handling, computational cost, and typical applications.\n* (Minor) Clarify how this review differs from previous surveys in offline reinforcement learning or design bench evaluations (for example Trabucco et al., 2022).\n* (Optional) Expand the section on LLM alignment and AI safety with concrete examples, or explicitly label it as a speculative outlook.\n* (Optional) Improve figure formatting and typography consistency to enhance readability and accessibility.", "broader_impact_concerns": "No significant ethical or dual use concerns are evident.\nThe brief mention of AI safety and alignment is conceptual rather than operational.\nIf retained, it would be useful to acknowledge potential dual use aspects of generative optimization (for example molecule generation) and emphasize responsible data usage.", "additional_comments": "This is a timely and well written survey that organizes a fragmented literature into a clear and coherent framework.\nThe manuscript is already strong and close to acceptance.\nIncorporating a small comparative table, clarifying differentiation from earlier surveys, and tightening speculative sections would further strengthen its contribution as a lasting reference for offline MBO research.", "extra_scores": {}, "extra_text": {}}, {"review_id": "ioPf3OlaSb", "reviewer": "Reviewer_ekiT", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper provides a comprehensive survey of offline model-based optimization, systematizing existing methods in both surrogate modeling and generative modeling, together with benchmarks and evaluation metrics.\n\n### ***Strengths*** \n- The paper covers a broad range of recent studies spanning surrogate and generative modeling approaches, offering readers a useful overview of current research progress.\n- The discussion of benchmarks, datasets, and evaluation metrics can serve as a practical reference for newcomers entering the field.\n\n### ***Weaknesses*** \nCompared with the previous submission, this revision does not introduce substantial updates. It does not address the core issues raised in the earlier review.\n- The survey is still a categorization and summary of past work. It does not provide insights into the rationale behind different approaches or discuss their practical implications.", "claims_and_evidence_yn": "No", "claims_explanation": "As a review article, the paper is expected to provide insights into the ***motivations behind prior work—clarifying why different methods were developed and what key challenges they address***. However, the current version does not offer a unified or logically grounded perspective that helps readers understand the underlying principles connecting these approaches in offline MBO. Instead, the contribution remains largely a high-level categorization and description of existing methods.\n\nSince LLMs today can already generate competent summaries of related work, a review paper must go beyond simple categorization and provide deeper expert insight into motivations, underlying principles, and practical implications — which this submission currently lacks.", "audience_yn": "Yes", "audience_explanation": "Researchers working on data-driven design and black-box optimization may find the collected references useful", "requested_changes": "Please see the weaknesses and explanation provided above.", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "nMijHRXSHr", "reviewer": "Reviewer_JsRc", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "**Summary**\n\nThis paper provides a comprehensive literature review of offline model-based optimization (MBO). This field aims to optimize a black-box function based on a pre-defined dataset of input-output pairs and some offline-specific model. The paper investigates different aspects of offline MBO, including problem definition/classification, dataset (benchmark), existing approaches, and future direction.", "claims_and_evidence_yn": "No", "claims_explanation": "**Weaknesses**\n\nAs a newcomer to the field of offline MBO (the target audience of the paper), after reading through the survey, I have several concerns that I would like the authors to address.\n\n1. Inconsistency of notation/terminology\n\n   This is one of the most significant issues of this survey. As a newcomer in the field, I expect the survey to serve as a self-contained guide through the basic problem setup and the high-level ideas behind the existing approaches. However, this survey contains several inconsistencies in terms of notation and terminology, making it sometimes confusing to read. Below, I detail some of the problems I noticed.\n\n   - Offline MBO and offline black-box optimization\n\n     As suggested by the title, this paper is a survey of offline model-based optimization. However, this survey mixes up offline MBO and offline black-box optimization in many places. Although in my understanding, offline MBO builds on offline black-box optimization, it would be beneficial to be precise about their relation (e.g., offline MBO is a method for offline black-box optimization). Otherwise, it looks confusing when the paper goes back and forth between these two notions.\n\n   - Use of \"surrogate model\"\n\n     The concept of surrogate model appears in two places in this paper, but they seem to carry different meanings. In the **Benchmark** section, surrogate models refer to the approximation of the true oracle, which is different from their meaning in the **Surrogate modeling** section. This inconsistency can cause much confusion when reading the paper for the first time.\n\n   - Terminology abbreviation/Undefined terminology\n\n     Some of the terminologies are abbreviated, but they are not properly defined when they appear for the first time. For example, out-of-distribution (OOD), upper confidence bound (UCB), GAN.\n\n     Besides, the paper seems to introduce a number of concepts without explaining their definition. For example, \"spurious optimization\", \"epistemic uncertainty\", \"aleatoric\", \"lower confidence bound\", \"many-objective\", \"COMs\"\n\n2. Duplicate contents\n\n   Some of the contents of the survey are repeated many times. For example, a **Generative modeling** paragraph appears in the **Problem definition** section. These repetitions often make things unclear.\n\n3. Inaccurate references\n\n   I also find a number of inaccuracies in the references of the paper. Since this paper is a literature review, I strongly recommend that the authors carefully check all the references in the paper and ensure they are timely and accurate. You can use an LLM to assist in transforming the bib file.\n\n   - Some of the journal names are not correct. For example,\n     1. (Capitalization) Journal of chemical theory and computation\n     2. (Capitalization) Journal of chemical information and modeling\n     3. (Capitalization) PMLR\n     4. (Capitalization) Operations research\n     5. (Abbreviation) Proc. Adv. Neur. Inf. Proc. Syst. \n     6. There are numerous issues like this. Please carefully check.\n   - Some papers are already published, but the outdated arXiv version is used. For example, \n     1. Posterior inference with diffusion models for high-dimensional black-box optimization\n     2. On the design fundamentals of diffusion models\n     3. AffinityFlow: guided flows for antibody affinity maturation\n     4. Differentiable scaffolding tree for molecular optimization\n   - There are several duplicated references.\n     1. Survey of variation in human transcription factors reveals prevalent DNA binding changes.\n     2. Human 5 utr design and variant effect prediction from a massively parallel translation assay.\n     3. Local fitness landscape of the green fluorescent protein\n     4. Objectives and methods in multi-objective routing problems: a survey and classification scheme\n\nOverall, I find this survey paper, in its current form, is not sufficiently well-written and friendly for a newcomer to the field. I suggest the authors carefully address the above issues before considering publishing it.\n\n**Questions**\n\n1. In the **Evaluation Metric** section, only usefulness is commonly used in the literature. Although you mentioned that it is \"partly due to the relative ease of demonstrating improvements in usefulness\", I find the motivation behind the other two metrics is not very clear. Could you elaborate more on them?\n2. The section **Sampling Strategy** mostly discusses how to optimize the surrogate model. Why is it called \"sampling strategy\"?\n3. The **Conclusion** section (**Robust and Realistic Benchmarking**) does not follow the structure of the previous discussion. Please consider reorganizing it.\n\n**Minor issues**\n\n1. Page 1\n\n   \"offline black-box optimization\" is not properly capitalized throughout the paper.\n\n2. Page 1\n\n   \"beyond training data\", \"training distribution\". The concept of \"training data\" is not explicitly defined.\n\n3. Page 1\n\n   \"High-performing\", \"high-performance\", and \"high-value\" are used inconsistently throughout the paper.\n\n4. Page 3\n\n   Sampling strategy/Number of **itertions** => Sampling strategy/Number of **iterations**.\n\n5. Page 4\n\n   Incorrect full stop in equation (1).\n\n6. Page 6\n\n   \"the focus is on a single property\". The meaning of \"property\" here is unclear.\n\n7. Page 6\n\n   \"online black-box optimization\" is not properly capitalized\n\n8. Page 6\n\n   The order of exploration and exploitation can be exchanged.\n\n9. Page 8\n\n   \"can be arbitrarily large (Any)\" is unclear.\n\n10. Page 8\n\n    \"(as indicated in parentheses)\" is unclear.\n\n11. Page 8\n\n    The definition of \"DTLZ, Omnitest, VLMOP, and ZDT\" is not given.\n\n12. Page 10\n\n    materials science => material science.\n\n13. Page 11\n\n    The description of the **DNA** bullet point is not clear. \n\n14. Page 11\n\n    I don't think highly technical terms like \"CHEMBL3885882\" should appear here.\n\n15. Page 12\n\n    Why is \"leading to higher evaluation costs\" discussed as \"Limited search space\"?\n\n16. Page 18\n\n    employs a variational autoencoder => employ a variational autoencoder.\n\n17. Page 19\n\n    Why does scaling by $\\sqrt{d}$ compensate for the increase in the gradient norm? Intuitively, one should decrease the stepsize when the gradient norm becomes too large.\n\n18. Page 20\n\n    Is there a reference for \"necessitate a smaller $T$\"?\n\n19. Page 21\n\n    MBO is redefined\n\n20. Page 21, 22\n\n    The format of the boldface letters is inconsistent in the **Conditional generation** section.", "audience_yn": "Yes", "audience_explanation": "**Strength**\n\nThis survey paper is timely and easy to follow.", "requested_changes": "See **Weaknesses** and **Questions/Minor issues**", "broader_impact_concerns": "N/A.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)