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Learning Surrogates for Offline Black-Box Optimization via Gradient Matching
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Proves a worst-case bound on the optimization gap of gradient search on a learned surrogate in terms of gradient mismatch, and proposes MATCH-OPT, which trains surrogates by matching gradients along monotonic offline trajectories plus a value regression term.
Problem
Offline black-box optimization: surrogate models learned from offline data are inaccurate outside the data, so gradient search on them can land far from true optima; the relation between surrogate gradient error and optimization performance gap is unclear.
Approach
Bounds the performance gap of surrogate-guided gradient ascent by the max gradient discrepancy between surrogate and target, and trains the surrogate to match gradients using line-integral finite differences between offline point pairs (no extra queries), combined with a value regression regularizer over monotonic synthetic trajectories.
Key results
- MATCH-OPT achieves the lowest MNR at the 100th percentile (0.283) versus 0.367 for the next best listed value in the table (COMS 0.467 is second-lowest per text), and best on DKitty (0.957).
- At the 50th percentile, MATCH-OPT attains MNR 0.350, the best among the compared methods, and best on Hopper (0.393).
- Ablation: adding the regression regularizer improves over no-regularizer on 4 of 6 tasks at both percentiles.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add regression (value-matching) regularizer along synthetic monotonic trajectories to gradient matching loss (ablation) | MATCH-OPT · Design-bench (6 tasks), 100th percentile | score: better on 4/6 tasks (Ant, DKitty, Tf8 up; Hopper up; SCon and Tf10 down) | Mixed |
| add regression (value-matching) regularizer along synthetic monotonic trajectories to gradient matching loss (ablation) | MATCH-OPT · Design-bench (6 tasks), 50th percentile | score: better on Ant, DKitty, Hopper, Tf8; worse on SCon (0.471 to 0.439) and Tf10 (0.768 to 0.720) | Mixed |
| gradient matching loss on monotonic trajectories (MATCH-OPT) versus baselines | MATCH-OPT · Design-bench MNR, 100th percentile | mean normalized rank (lower better): MNR 0.283 vs next best COMS 0.467 | Helped |
| gradient matching loss on monotonic trajectories (MATCH-OPT) versus baselines | MATCH-OPT · Design-bench MNR, 50th percentile | mean normalized rank (lower better): MNR 0.350 (best among methods) | Helped |
| MATCH-OPT versus baselines on Hopper at 100th percentile | MATCH-OPT · Design-bench Hopper, 100th percentile | score: 1.572 vs COMS 2.270 (rank 3) | Mixed |
| MATCH-OPT on Tf10 at 100th percentile | MATCH-OPT · Design-bench Tf10, 100th percentile | score: 0.924 vs best 0.968 (Ens-Mean), rank 6 | Hurt |
| gradient matching surrogate with theory-motivated loss on OOD gradient estimation (Shekel function, 4-d) | MATCH-OPT vs standard regression · Shekel OOD synthetic gradient estimation error | gradient estimation error | Helped |
Surprising findings
- Ablation shows the regression regularizer does not help uniformly; no-regularizer is better on SCon and Tf10 at the 100th percentile.
- No single method is best on more than two task domains; MATCH-OPT is not top-ranked on SCon or Tf10 at the 50th percentile (rank 6).
Limitations
- Theoretical bound is worst-case and the bound's tightness relies on small learning rate (λ ≤ 1/m); the paper admits the regularizer-related tighter condition is not enforced in training.
- MATCH-OPT does not win on several tasks at the 50th percentile (e.g., SCon, Tf10 rank 6).
Experimental setup
Datasets: Ant Morphology D'Kitty Morphology Hopper Controller Superconductor TF-Bind-8 TF-Bind-10
Benchmarks: Ant DKitty Hopper SCon TF8 TF10
Metrics: 100th percentile performance 50th percentile performance mean normalized rank (MNR)
Baselines: GA Ens-Mean Ens-Min CMA-ES MINS CbAS RoMA BONET COMs
Builds on: design-bench COMs RoMA BONET
Closest papers by meaning
- Boosting Offline Optimizers with Surrogate Sensitivity (ICML 2024 · similarity 0.94)
- Offline Model-Based Optimization via Policy-Guided Gradient Search (AAAI 2024 · similarity 0.92)
- Incorporating Surrogate Gradient Norm to Improve Offline Optimization Techniques (NeurIPS 2024 · similarity 0.91)
- ROOT: Rethinking Offline Optimization as Distributional Translation via Probabilistic Bridge (NeurIPS 2025 · similarity 0.90)
- Offline Model-Based Optimization by Learning to Rank (ICLR 2025 · similarity 0.89)
- Guided Trajectory Generation with Diffusion Models for Offline Model-based Optimization (NeurIPS 2024 · similarity 0.87)
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