Title: ROOT: Rethinking Offline Optimization as Distributional Translation via Probabilistic Bridge
Venue: NeurIPS 2025
Accepted: yes
Keywords: Offline Optimization

Diffusion Model

Probabilistic Method
Abstract: This paper studies the black-box optimization task which aims to find the maxima of a black-box function using a static set of its observed input-output pairs. This is often achieved via learning and optimizing a surrogate function with that offline data. Alternatively, it can also be framed as an inverse modeling task that maps a desired performance to potential input candidates that achieve it. Both approaches are constrained by the limited amount of offline data. To mitigate this limitation, we introduce a new perspective that casts offline optimization as a distributional translation task. This is formulated as learning a probabilistic bridge transforming an implicit distribution of low-value inputs (i.e., offline data) into another distribution of high-value inputs (i.e., solution candidates). Such probabilistic bridge can be learned using low- and high-value inputs sampled from synthetic functions that resemble the target function. These synthetic functions are constructed as the mean posterior of multiple Gaussian processes fitted with different parameterizations on the offline data, alleviating the data bottleneck. The proposed approach is evaluated on an extensive benchmark comprising most recent methods, demonstrating significant improvement and establishing a new state-of-the-art performance. Our code is publicly available at https://github.com/cuong-dm/ROOT.


Peer reviews:
comments: SUMMARY:
This paper tackles offline black-box optimization by proposing a novel framework that treats the task as a distributional translation problem—from low-performing to high-performing inputs. Instead of relying solely on scarce offline data, it learns a probabilistic bridge using synthetic functions, constructed as averaged Gaussian processes fit to the data. This approach improves generalization and achieves state-of-the-art performance on benchmark tasks.

STRENGTHS AND WEAKNESSES:
Strengths: The idea of leveraging synthetic data to learn a mapping from low- to high-performing inputs is compelling. The results are strong, and I particularly appreciate the focus on addressing the core challenge of offline black-box optimization—data scarcity. This paper offers a promising direction to mitigate that limitation.

Weaknesses: One potential concern is that the synthetic functions may not closely reflect real-world tasks, such as biological sequence design. Additionally, the paper appears to overlook a recent and relevant survey in this area: Offline Model-Based Optimization: Comprehensive Review (https://arxiv.org/abs/2503.17286).

QUESTIONS:
See Strengths And Weaknesses

LIMITATIONS:
See Strengths And Weaknesses
TITLE: Official Review
CLARITY: 4
IMPACT: 3
ORIGINALITY: 3
DATE: 2025-06-04

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes ROOT, a new framework for offline black-box optimization that formulates the problem as a probabilistic bridge between a support distribution (from offline data) and an unknown optimal distribution. The authors frame offline optimization as learning a time-indexed trajectory in distribution space, connecting the initial offline data distribution to the target high-value design distribution. ROOT leverages variational inference to approximate this bridge and instantiates a diffusion-like architecture to model the intermediate transitions. The authors evaluate ROOT on offline molecule and biological sequence optimization tasks and compare against existing optimization baselines.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n- The idea of framing offline optimization as a probabilistic distributional bridge is creative and provides a new generative modeling perspective on offline design problems.\n\n- The ROOT architecture is flexible and can incorporate different score functions (e.g., predictive surrogates) to guide optimization, making it potentially extensible across various problem domains.\n\n- ROOT performs competitively on molecule and sequence tasks, demonstrating that the proposed formulation is viable in practice.\n\nWeaknesses\n- Theory–practice gap: The proposed variational formulation and bridge process are theoretically interesting but lack formal results (e.g., guarantees, convergence bounds).\n\n- Architectural details underexplained: Some implementation choices (e.g., score function choices, transition structure) would benefit from more ablation or motivation.\n\nQUESTIONS:\n- How robust is ROOT to poor offline data coverage? Have you tested performance under varying dataset support quality?\n\n- Can you clarify the computational cost of ROOT compared to other diffusion-based energy-based approaches?\n\n- Are there formal convergence or generalization guarantees that can support the ROOT framework theoretically?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 5, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper focuses on offline black-box optimization, which aims to maximize an objective function solely given an offline dataset. Previous works built mapping either from $x$ to $y$ or from $y$ to $x$, while this paper rethinks the optimization as from $x_{low}$ to $x_{high}$ (distributional translation as mentioned in the paper), which can be modeled by a probabilistic bridge model (initiated as a diffusion model). It utilizes Gaussian processes to derive synthetic data for diffusion training, then obtain the final solutions given solutions for the offline dataset after the model is trained.\n\nSTRENGTHS AND WEAKNESSES:\n## Strengths\n\n- The usage of diffusion models in offline optimization is novel.\n- The modeling of mapping between $x$s **with different qualities** is intuitive.\n- The experimental evaluations are comprehensive and clearly demonstrate the effectiveness of this paper.\n- The implementation code is clear.\n\n## Weaknesses\n\n- Based on my comprehension, constructing a mapping between different $x$s is also been employed by recent works [1-2] (although they do not project from $x_{low}$ to $x_{high}$). Relevant discussion is needed.\n\n## References\n\n[1] From Function to Distribution Modeling: A PAC-Generative Approach to Offline Optimization. arXiv 2024.\n\n[2] Design Editing for Offline Model-based Optimization. TMLR 2025.\n\nQUESTIONS:\n- Why do you conduct gradient ascent / descent on the mean functions of GP to obtain the synthetic data? As GP not only models the value but also quantifies the uncertainty. If the offline dataset also has limited coverage, only focusing on mean functions (without integrating the uncertainty of GP) could also lead to unfavorable data. Thus, I suggest comparing constructing synthetic data on UCB or LCB acquisition functions.\n- In Introduction and Section 5, you mention that previous methods remain constrained by limited data coverage. Why does your method address this challenge? More discussions are needed.\n- How does your proposed method perform under different data scarcities (not only the few-shot settings in Table 4)?\n\nLIMITATIONS:\nSee Weaknesses and Questions above. I am willing to increase my score once my concerns are addressed.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes ROOT, an offline black‑box optimization framework that recasts the task as a distributional translation problem. A probabilistic bridge, inspired by diffusion but conditioned on both source and target points, is trained on synthetic low‑ and high‑value design pairs generated from an ensemble of Gaussian‑process posterior means fitted to the offline data. Once trained, the bridge is run backward from the best offline samples to produce improved candidates. Experiments on four Design‑Bench tasks and three RNA inverse‑folding tasks report new state‑of‑the‑art results and extensive ablations support each design choice.\n\nSTRENGTHS AND WEAKNESSES:\nQuality: Empirical work is thorough, with eight independent runs, multiple percentiles, and ablations on step size, GP ensemble size, and data budgets. However, the method is empirically driven; there is no theoretical guarantee that the learned bridge preserves function maxima, and some critical implementation details (e.g., GP kernel hyper‑parameter grids, training compute) are only in the appendix. \n\nClarity: The core idea is clearly motivated and the probabilistic bridge derivation is explicit, yet the paper is very long, and key intuition is buried in implementation, which may hinder reproducibility. \n\nSignificance: Achieving uniform gains across both continuous robot morphology and discrete sequence design benchmarks suggests practical impact, but the community still lacks evidence that gains transfer to harder high‑dimensional or noisy settings. \n\nOriginality: Framing offline optimization explicitly as distributional translation via a bridge that conditions on both endpoints is novel, though it builds heavily on recent diffusion‑based optimizers and GP‑assisted pretraining.\n\nQUESTIONS:\nPlease clarify the computational cost of fitting eight hundred GPs versus a single large GP ensemble and how this scales beyond ten thousand offline points; discuss whether fewer but higher‑rank kernels could suffice. \n\nExplain how ROOT would handle objectives with strong measurement noise, since synthetic labels come from deterministic GP means. \n\nProvide results on at least one truly high‑dimensional continuous task (e.g., 1000‑dim design) to assess scalability. \n\nDescribe how sensitive performance is to the choice of Brownian‑bridge parameters and whether other kernel choices were tried. \n\nA detailed comparison with very recent diffusion‑based baselines such as DiGBO or DM‑BO would strengthen the empirical claim.\n\nLIMITATIONS:\nThe authors list data and compute limitations and note lack of theory, but they should also acknowledge that GP‑derived synthetic data may embed biases of the initial kernel, potentially restricting exploration.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-05"}