GenAI4ELab/papercli-papers huggingface dataset:
Learning with Linear Function Approximations in Mean-Field Control
Authors: Erhan Bayraktar; Ali Devran Kara
Venue: JMLR 2025 (main)

Abstract: The paper focuses on mean-field type multi-agent control problems with finite state and action spaces where the dynamics and cost structures are symmetric and homogeneous, and are affected by the distribution of the agents. A standard solution method for these problems is to consider the infinite population limit as an approximation and use symmetric solutions of the limit problem to achieve near optimality. The control policies, and in particular the dynamics, depend on the population distribution in the finite population setting, or the marginal distribution of the state variable of a representative agent for the infinite population setting. Hence, learning and planning for these control problems generally require estimating the reaction of the system to all possible state distributions of the agents. To overcome this issue, we consider linear function approximation for the control problem and provide coordinated and independent learning methods. We rigorously establish error upper bounds for the performance of learned solutions. The performance gap stems from (i) the mismatch due to estimating the true model with a linear one, and (ii) using the infinite population solution in the finite population problem as an approximate control. The provided upper bounds quantify the impact of these error sources on the overall performance.
On the Convergence of Projected Policy Gradient for Any Constant Step Sizes
Authors: Jiacai Liu; Wenye Li; Dachao Lin; Ke Wei; Zhihua Zhang
Venue: JMLR 2025 (main)

Abstract: Projected policy gradient (PPG) is a basic policy optimization method in reinforcement learning. Given access to exact policy  evaluations, previous studies have established the sublinear convergence of PPG for sufficiently small step sizes based on the smoothness and the gradient domination properties of the value function. However, as the step size  goes to infinity, PPG reduces to the classic policy iteration method, which suggests the convergence of PPG even for large step sizes. In this paper, we fill this gap and show that PPG admits a sublinear convergence for any constant step sizes. Due to the existence of the state-wise visitation measure in the expression of policy gradient, the existing optimization-based analysis framework for a preconditioned version of PPG (i.e., projected Q-ascent) is not applicable, to the best of our knowledge. Instead, we proceed the proof by computing the state-wise improvement lower bound of PPG based on its inherent structure. In addition, the finite iteration convergence of PPG for any constant step size is further established, which is also new.
Linear Separation Capacity of Self-Supervised Representation Learning
Authors: Shulei Wang
Venue: JMLR 2025 (main)

Abstract: Recent advances in self-supervised learning have highlighted the efficacy of data augmentation in learning data representation from unlabeled data. Training a linear model atop these enhanced representations can yield an adept classifier. Despite the remarkable empirical performance, the underlying mechanisms that enable data augmentation to unravel nonlinear data structures into linearly separable representations remain elusive. This paper seeks to bridge this gap by investigating under what conditions learned representations can linearly separate manifolds when data is drawn from a multi-manifold model. Our investigation reveals that data augmentation offers additional information beyond observed data and can thus improve the information-theoretic optimal rate of linear separation capacity. In particular, we show that self-supervised learning can linearly separate manifolds with a smaller distance than unsupervised learning, underscoring the additional benefits of data augmentation. Our theoretical analysis further underscores that the performance of downstream linear classifiers primarily hinges on the linear separability of data representations rather than the size of the labeled data set, reaffirming the viability of constructing efficient classifiers with limited labeled data amid an expansive unlabeled data set.
Relaxed Gaussian Process Interpolation: a Goal-Oriented Approach to Bayesian Optimization
Authors: SÃ©bastien J. Petit; Julien Bect; Emmanuel Vazquez
Venue: JMLR 2025 (main)

Abstract: This work presents a new procedure for obtaining predictive distributions in the context of Gaussian process (GP) modeling, with a relaxation of the interpolation constraints outside ranges of interest: the mean of the predictive distribution no longer necessarily interpolates the observed values when they are outside ranges of interest, but is simply constrained to remain outside. This method called relaxed Gaussian process (reGP) interpolation provides better predictive distributions in ranges of interest, especially in cases where a stationarity assumption for the GP model is not appropriate. It can be viewed as a goal-oriented method and becomes particularly interesting in Bayesian optimization, for example, for the minimization of an objective function, where good predictive distributions for low function values are important. When the expected improvement criterion and reGP are used for sequentially choosing evaluation points, the convergence of the resulting optimization algorithm is theoretically guaranteed (provided that the function to be optimized lies in the reproducing kernel Hilbert space attached to the known covariance of the underlying Gaussian process). Experiments indicate that using reGP instead of stationary GP models in Bayesian optimization is beneficial.
Calibrated Inference: Statistical Inference that Accounts for Both Sampling Uncertainty and Distributional Uncertainty
Authors: Yujin Jeong; Dominik RothenhÃ¤usler
Venue: JMLR 2025 (main)

Abstract: How can we draw trustworthy scientific conclusions? One criterion is that a study can be replicated by independent teams. While replication is critically important, it is arguably insufficient. If a study is biased for some reason and other studies recapitulate the approach then findings might be consistently incorrect. It has been argued that trustworthy scientific conclusions require disparate sources of evidence. However, different methods might have shared biases, making it difficult to judge the trustworthiness of a result. We formalize this issue by introducing a "distributional uncertainty model", wherein dense distributional shifts emerge as the superposition of numerous small random changes. The distributional perturbation model arises under a symmetry assumption on distributional shifts and is strictly weaker than assuming that the data is i.i.d. from the target distribution. We show that a stability analysis on a single data set allows us to construct confidence intervals that account for both sampling uncertainty and distributional uncertainty.
Decentralized Sparse Linear Regression via Gradient-Tracking
Authors: Marie Maros; Gesualdo Scutari; Ying Sun; Guang Cheng
Venue: JMLR 2025 (main)

Abstract: We study   sparse linear regression over a network of agents, modeled as an undirected  graph without a center node. The estimation of the $s$-sparse parameter is  formulated as a constrained LASSO problem wherein each agent   owns a subset of the $N$ total   observations. We analyze the convergence rate and statistical guarantees of a distributed projected gradient tracking-based algorithm under high-dimensional scaling, allowing the ambient  dimension $d$ to grow with (and possibly exceed) the sample size $N$. Our theory shows that, under standard   notions of restricted strong convexity and smoothness of the average loss functions,  suitable conditions on the network connectivity  and algorithm tuning, the distributed algorithm converges   globally at a   linear rate to an estimate that is within the centralized   statistical precision  of the model, $O(s\log d/N)$. When $s\log d/N=o(1)$, a condition necessary for statistical consistency, an $\varepsilon$-optimal solution is attained after  ${O}(\kappa \log (1/\varepsilon))$ gradient computations  and $O(\kappa/(1-\rho) \log (1/\varepsilon))$  communication rounds,
where $\kappa$ is the restricted condition number of the loss function and $\rho$ measures the network connectivity. The computation cost matches that of  the centralized projected gradient algorithm despite  having data distributed; whereas the communication rounds reduce as the network connectivity improves. Overall, our study   reveals  interesting connections between statistical efficiency, network connectivity and topology, and  convergence rate in  the high dimensional setting.
Optimal subsampling for high-dimensional partially linear models via machine learning methods
Authors: Yujing Shao; Lei Wang; Heng Lian; Haiying Wang
Venue: JMLR 2025 (main)

Abstract: In this paper, we explore optimal subsampling strategies for estimating the parametric regression coefficients in partially linear models with unknown nuisance functions involving high-dimensional and potentially endogenous covariates. To address model misspecifications and the curse of dimensionality, we leverage flexible machine learning (ML) techniques to estimate the unknown nuisance functions.  By constructing an unbiased subsampling Neyman-orthogonal score function, we eliminate regularization bias. A two-step algorithm is then used to obtain appropriate ML estimators of the nuisance functions, mitigating the risk of over-fitting. Using martingale techniques, we establish the unconditional consistency and asymptotic normality of the subsample estimators. Furthermore, we derive optimal subsampling probabilities, including A-optimal and L-optimal probabilities as special cases. The proposed optimal subsampling approach is extended to partially linear instrumental variable models to account for potential endogeneity through instrumental variables.  Simulation studies and an empirical analysis of the Physicochemical Properties of Protein Tertiary Structure dataset demonstrate the superior performance of our subsample estimators.
Operator Learning for Hyperbolic PDEs
Authors: Christopher Wang; Alex Townsend
Venue: JMLR 2025 (main)

Abstract: We construct the first rigorously justified probabilistic algorithm for recovering the solution operator of a hyperbolic partial differential equation (PDE) in two variables from input-output training pairs. The primary challenge of recovering the solution operator of hyperbolic PDEs is the presence of characteristics, along which the associated Green's function is discontinuous. Therefore, a central component of our algorithm is a rank detection scheme that identifies the approximate location of the characteristics. By combining the randomized singular value decomposition with an adaptive hierarchical partition of the domain, we construct an approximant to the solution operator using $O(\Psi_\epsilon^{-1}\epsilon^{-7}\log(\Xi_\epsilon^{-1}\epsilon^{-1}))$ input-output pairs with relative error $O(\Xi_\epsilon^{-1}\epsilon)$ in the operator norm as $\epsilon\to0$, with high probability. Here, $\Psi_\epsilon$ represents the existence of degenerate singular values of the solution operator, and $\Xi_\epsilon$ measures the quality of the training data. Our assumptions on the regularity of the coefficients of the hyperbolic PDE are relatively weak given that hyperbolic PDEs do not have the "instantaneous smoothing effect" of elliptic and parabolic PDEs, and our recovery rate improves as the regularity of the coefficients increases. We also include numerical experiments which corroborate our theoretical findings.
An Adaptive Parameter-free and Projection-free Restarting Level Set Method for Constrained Convex Optimization Under the Error Bound Condition
Authors: Qihang Lin; Negar Soheili; Runchao Ma; Selvaprabu Nadarajah
Venue: JMLR 2025 (main)

Abstract: Recent efforts to accelerate first-order methods have focused on convex optimization problems that satisfy a geometric property known as error-bound condition, which covers a broad class of problems, including piece-wise linear programs and strongly convex programs. Parameter-free first-order methods that employ projection-free updates have the potential to broaden the benefit of acceleration. Such a method has been developed for unconstrained convex optimization but is lacking for general constrained convex optimization. We propose a parameter-free level-set method for the latter constrained case based on projection-free subgradient method that exhibits accelerated convergence for problems that satisfy an error-bound condition. Our method maintains a separate copy of the level-set sub-problem for each level parameter value and restarts the computation of these copies based on objective function progress. Applying such a restarting scheme in a level-set context is novel and results in an algorithm that dynamically adapts the precision of each copy. This property is key to extending prior restarting methods based on static precision that have been proposed for unconstrained convex optimization to handle constraints. We report promising numerical performance relative to benchmark methods.
Are Ensembles Getting Better All the Time?
Authors: Pierre-Alexandre Mattei; Damien Garreau
Venue: JMLR 2025 (main)

Abstract: Ensemble methods combine the predictions of several base models. We study whether or not including more models always improves their average performance. This question depends on the kind of ensemble considered, as well as the predictive metric chosen. We focus on situations where all members of the ensemble are a priori expected to perform equally well, which is the case of several popular methods such as random forests or deep ensembles. In this setting, we show that ensembles are getting better all the time if, and only if, the considered loss function is convex. More precisely, in that case, the loss of the ensemble is a decreasing function of the number of models. When the loss function is nonconvex, we show a series of results that can be summarised as: ensembles of good models keep getting better, and ensembles of bad models keep getting worse. To this end, we prove a new result on the monotonicity of tail probabilities that may be of independent interest. We illustrate our results on a  medical problem (diagnosing melanomas using neural nets) and a âwisdom of crowdsâ experiment (guessing the ratings of upcoming movies).
Variational Inference for Uncertainty Quantification: an Analysis of Trade-offs
Authors: Charles C. Margossian; Loucas Pillaud-Vivien; Lawrence K. Saul
Venue: JMLR 2025 (main)

Abstract: Given an intractable distribution $p$, the problem of variational inference (VI) is to find the best approximation from some more tractable family $Q$. Commonly, one chooses $Q$ to be a family of factorized distributions (i.e., the mean-field assumption), even though $p$ itself does not factorize. We show that this mismatch leads to an impossibility theorem: if $p$ does not factorize, then any factorized approximation $q\!\in\!Q$ can correctly estimate at most one of the following three measures of uncertainty: (i) the marginal variances, (ii) the marginal precisions, or (iii) the generalized variance (which for elliptical distributions is closely related to the entropy). In practice, the best variational approximation in $Q$ is found by minimizing some divergence $D(q,p)$ between distributions, and so we ask: how does the choice of divergence determine which measure of uncertainty, if any, is correctly estimated by VI? We consider the classic Kullback-Leibler divergences, the more general $\alpha$-divergences, and a score-based divergence which compares $\nabla \log p$ and $\nabla \log q$. We thoroughly analyze the case where $p$ is a Gaussian and $q$ is a (factorized) Gaussian. In this setting, we show that all the considered divergences can be ordered based on the estimates of uncertainty they yield as objective functions for VI. Finally, we empirically evaluate the validity of this ordering when the target distribution $p$ is not Gaussian.
Reliever: Relieving the Burden of Costly Model Fits for Changepoint Detection
Authors: Chengde Qian; Guanghui Wang; Changliang Zou
Venue: JMLR 2025 (main)

Abstract: Changepoint detection typically relies on a grid-search strategy for optimal data segmentation. When model fitting itself is expensive, repeatedly fitting a model on every candidate segment dominates the computation. Existing approaches mitigate this by pruning the grid, thus reducing the number of segments (and model fits). We propose Reliever, which instead cuts the number of model fits directly and nests seamlessly within standard grid-search routines. Reliever fits a small, deterministic collection of proxy models and reuses them wherever they apply, making it compatible with a wide range of existing algorithms. For high-dimensional regression with changepoints, coupling Reliever with an optimal grid-search method yields changepoint and coefficient estimators that are rate-optimal up to a logarithmic factor. Extensive numerical experiments demonstrate that Reliever rapidly and accurately detects changepoints across a wide range of high-dimensional and nonparametric models.
BoFire: Bayesian Optimization Framework Intended for Real Experiments
Authors: Johannes P. DÃ¼rholt; Thomas S. Asche; Johanna Kleinekorte; Gabriel Mancino-Ball; Benjamin Schiller; Simon Sung; Julian Keupp; Aaron Osburg; Toby Boyne; Ruth Misener; Rosona Eldred; Chrysoula Kappatou; Robert M. Lee; Dominik Linzner; Wagner Steuer Costa; David Walz; Niklas Wulkow; Behrang Shafei
Venue: JMLR 2025 (main)

Abstract: Our open-source Python package BoFire combines Bayesian Optimization (BO) with other design of experiments (DoE) strategies focusing on developing and optimizing new chemistry. Previous BO implementations, for example as they exist in the literature or software, require substantial adaptation for effective real-world deployment in chemical industry. BoFire provides a rich feature-set with extensive configurability and realizes our vision of fast-tracking research contributions into industrial use via maintainable open-source software. Owing to quality-of-life features like JSON-serializability of problem formulations, BoFire enables seamless integration of BO into RESTful APIs, a common architecture component for both self-driving laboratories and human-in-the-loop setups. This paper discusses the differences between BoFire and other BO implementations and outlines ways that BO research needs to be adapted for real-world use in a chemistry setting.
Robust Point Matching with Distance Profiles
Authors: YoonHaeng Hur; Yuehaw Khoo
Venue: JMLR 2025 (main)

Abstract: Computational difficulty of quadratic matching and the Gromov-Wasserstein distance has led to various approximation and relaxation schemes. One of such methods, relying on the notion of distance profiles, has been widely used in practice, but its theoretical understanding is limited. By delving into the statistical complexity of the previously proposed method based on distance profiles, we show that it suffers from the curse of dimensionality unless we make certain assumptions on the underlying metric measure spaces. Building on this insight, we propose and analyze a modified matching procedure that can be used to robustly match points under a certain probabilistic setting. We demonstrate the performance of the proposed methods using simulations and real data applications to complement the theoretical findings. As a result, we contribute to the literature by providing theoretical underpinnings of the matching procedures based on distance invariants like distance profiles, which have been widely used in practice but rarely analyzed theoretically.
Mixtures of Gaussian Process Experts with SMC^2
Authors: Teemu HÃ¤rkÃ¶nen; Sara Wade; Kody Law; Lassi Roininen
Venue: JMLR 2025 (main)

Abstract: Gaussian processes are a key component of many flexible statistical and machine learning models. However, they exhibit cubic computational complexity and high memory constraints due to the need of inverting and storing a full covariance matrix. To circumvent this, mixtures of Gaussian process experts have been considered where data points are assigned to independent experts, reducing the complexity by allowing inference based on smaller, local covariance matrices. Moreover, mixtures of Gaussian process experts substantially enrich the model's flexibility, allowing for behaviors such as non-stationarity, heteroscedasticity, and discontinuities. In this work, we construct a novel inference approach based on nested sequential Monte Carlo samplers to simultaneously infer both the gating network and Gaussian process expert parameters. This greatly improves inference  compared to importance sampling, particularly in settings when a stationary Gaussian process is inappropriate,  while still being thoroughly parallelizable.
Decentralized Asynchronous Optimization with DADAO allows Decoupling and Acceleration
Authors: Adel Nabli; Edouard Oyallon
Venue: JMLR 2025 (main)

Abstract: DADAO is the first decentralized, accelerated, asynchronous, primal, first-order algorithm to minimize  a sum of $L$-smooth and $\mu$-strongly convex functions distributed over a network of size $n$.  Modeling the gradient updates and gossip communication procedures with separate independent Poisson Point Processes allows us to decouple the computation and communication steps, which can be run in parallel, while making the whole approach completely asynchronous. This leads to communication acceleration compared to synchronous approaches. Our method employs primal gradients and avoids using a multi-consensus inner loop and other ad-hoc mechanisms. By relating the smallest positive eigenvalue $1/\chi_1$ of the Laplacian matrix $\Lambda$  and the maximal resistance $\chi_2\leq \chi_1$ of the graph to a sufficient minimal communication rate, we show that  DADAO requires $\mathcal{O}(n\sqrt{\frac{L}{\mu}}\log(\frac{1}{\epsilon}))$ local gradients and only $\mathcal{O}(\sqrt{\chi_1\chi_2}\operatorname{Tr}\Lambda\sqrt{\frac{L}{\mu}}\log(\frac{1}{\epsilon}))$ communications to reach $\epsilon$-precision, up to logarithmic terms. Thus, we simultaneously obtain an accelerated rate for computations and communications, leading to an improvement over state-of-the-art works, our simulations further validating the strength of our relatively unconstrained method. Moreover, we propose a SDP relaxation to find the gossip rate of each edge minimizing the total number of communications for a given graph, resulting in faster convergence compared to standard approaches relying on uniform communication weights.