Black-Box Optimization From Small Offline Datasets via Meta Learning with Synthetic Tasks

Azza Fadhel; The Hung Tran; Trong Nghia Hoang; Jana Doppa

cs.LGApr 14, 2026

Black-Box Optimization From Small Offline Datasets via Meta Learning with Synthetic Tasks

Authors: Azza Fadhel, The Hung Tran, Trong Nghia Hoang, Jana Doppa

Organizations: School of EECS, Washington State University, Pullman, WA, USA

Abstract

We consider the problem of offline black-box optimization, where the goal is to discover optimal designs (e.g., molecules or materials) from past experimental data. A key challenge in this setting is data scarcity: in many scientific applications, only small or poor-quality datasets are available, which severely limits the effectiveness of existing algorithms. Prior work has theoretically and empirically shown that performance of offline optimization algorithms depends on how well the surrogate model captures the optimization bias (i.e., ability to rank input designs correctly), which is challenging to accomplish with limited experimental data. This paper proposes Surrogate Learning with Optimization Bias via Synthetic Task Generation (OptBias), a meta-learning framework that directly tackles data scarcity. OptBias learns a reusable optimization bias by training on synthetic tasks generated from a Gaussian process, and then fine-tunes the surrogate model on the small data for the target task. Across diverse continuous and discrete offline optimization benchmarks, OptBias consistently outperforms state-of-the-art baselines in small data regimes. These results highlight OptBias as a robust and practical solution for offline optimization in realistic small data settings.

Figures & tables

Figure 1: Conceptual illustration of gradient estimation error vs. fraction of training data on the Shekel-4D synthetic task. The surrogate is trained on 8,000 samples and evaluated on 2,000 test points; bars are colored red→green for higher→lower error. The gradient estimation error increases significantly in the small training data regime relative to the full (100 %) data.

Figure 2: Workflow overview of OptBias . First, we use a novel Sim4Opt procedure to generate synthetic functions which are similar to the oracle function. Then, we combine meta-learning with gradient matching ( MatchOpt ) to distill the common parts across gradient fields of the synthetic functions into a surrogate, thus implicitly aligning it with the (unobserved) gradient field of the oracle function.

	Benchmarks
Method	Ant	D’Kitty	TFBind8	RNA1	RNA2	RNA3	Mean Rank
$D_{best}$ from 1 $\%$ offline data	0.123	0.307	0.124	0.028	0.027	0.066	None
GA	0.734 ± 0.054	0.831 ± 0.034	0.782 ± 0.117	0.475 ± 0.134	0.497 ± 0.091	0.317 ± 0.072	5.17
MINs	0.767 ± 0.084	0.895 ± 0.011	0.762 ± 0.135	0.076 ± 0.062	0.019 ± 0.029	0.132 ± 0.059	7.67
COMs	0.908 ± 0.042	0.705 ± 0.012	0.438 ± 0.000	0.279 ± 0.059	0.278 ± 0.120	0.293 ± 0.044	6.08
DEMO	0.800 ± 0.150	0.845 ± 0.037	0.677 ± 0.168	0.166 ± 0.034	0.141 ± 0.045	0.295 ± 0.043	6.50

Table 1: Performance achieved by baselines under the limited data settings (using 1% of the offline dataset) across various benchmark tasks.

	Benchmarks
Method	Ant	D’Kitty	TFBind8	RNA1	RNA2	RNA3
OptBias (pre-training)	0.884 ± 0.043	0.932 ± 0.007	0.438 ± 0.000	0.129 ± 0.000	0.119 ± 0.000	0.166 ± 0.000
OptBias (meta-learning)	0.960 ± 0.017	0.947 ± 0.012	0.945 ± 0.024	0.503 ± 0.025	0.540 ± 0.113	0.450 ± 0.134

Table 2: Performance comparison between our proposed method OptBias , which uses meta-learning for surrogate training with synthetic data, and its variant, which replaces meta-learning with a pre-training procedure.

	Benchmarks
Method	Ant	D’Kitty	TFBind8	RNA1	RNA2	RNA3
OptBias w/ Random	0.701 ± 0.157	0.857 ± 0.058	0.882 ± 0.0548	0.493 ± 0.0458	0.532 ± 0.0549	0.518 ± 0.077
OptBias (ours)	0.960 ± 0.017	0.947 ± 0.012	0.945 ± 0.024	0.503 ± 0.025	0.540 ± 0.113	0.450 ± 0.134

Table 3: Performance comparison between our proposed method OptBias and its variant which replaces Sim4Opt with ExPT ’s data generation procedure.

Setting	ANT (mean $\pm$ std)	DKitty (mean $\pm$ std)
Matern Kernel	0.957 $\pm$ 0.004	0.898 $\pm$ 0.022
UCB Acquisition	0.937 $\pm$ 0.023	0.948 $\pm$ 0.010
Trajectory Length = 70	0.942 $\pm$ 0.016	0.947 $\pm$ 0.009
Lengthscale = 1.5	0.950 $\pm$ 0.008	0.871 $\pm$ 0.031
Lengthscale = 2.0	0.916 $\pm$ 0.063	0.956 $\pm$ 0.007
OptBias (main results)	0.960 $\pm$ 0.010	0.947 $\pm$ 0.012

Table 4: Ablation study on GP design choices used in the Sim4Opt synthetic task generation procedure. Results show final optimization performance of OptBias averaged over four seeds.

Figure 3: Empirical distribution of oracle-evaluated $y$ -values (objective function values) over synthetic designs generated by multiple Gaussian Processes.

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

	Benchmarks
Method	Ant	D’Kitty	TFBind8	Mean Rank
$D_{best}$ from 1 $\%$ offline data	0.123	0.307	0.124	None
DDOM	0.324 ± 0.024	0.746 ± 0.012	0.771 ± 0.121	5.33
Tri-mentoring	0.831 ± 0.015	0.928 ± 0.008	0.645 ± 0.030	4.0
BDI	0.298 ± 0.000	0.728 ± 0.000	0.447 ± 0.000	5.67
RGD	0.870 ± 0.022	0.888 ± 0.015	0.890 ± 0.057	3.17

Appendix

Table 5: Performance achieved by baselines under the limited data settings (using 1% of the offline dataset) across various benchmark tasks.

Method ( $K$ )	Ant	D’Kitty	TFBind8	RNA1	RNA2	RNA3	Mean Rank
OptBias (128)	0.960 ± 0.017 ( 1 )	0.947 ± 0.012 ( 1 )	0.945 ± 0.024 ( 1 )	0.503 ± 0.025 (2)	0.540 ± 0113 ( 1 )	0.450 ± 0.134 (4)	1.67
OptBias (64)	0.912 ± 0.082 (3)	0.938 ± 0.029 (2)	0.916 ± 0.087 (2)	0.541 ± 0.149 ( 1 )	0.531 ± 0.115 (2)	0.550 ± 0.035 ( 1 )	1.83
OptBias (16)	0.926 ± 0.060 (2)	0.906 ± 0.050 (3)	0.855 ± 0.080 (4)	0.437 ± 0.137 (3)	0.453 ± 0.136 (3)	0.539 ± 0.044 (2)	2.83
OptBias (8)	0.823 ± 0.130 (4)	0.890 ± 0.081 (4)	0.871 ± 0.060 (3)	0.368 ± 0.214 (4)	0.377 ± 0.183 (4)	0.471 ± 0.088 (3)	3.67

Appendix

Table 7: Performance of OptBias under different

K

across Design-Bench tasks. Higher is better. Bold marks the best value (and its rank) per task, and the best mean rank.

Black-Box Optimization

Black-box optimization finds high-quality solutions when objectives can only be queried, not directly analyzed or differentiated.

See all 177 papers

Support-Proximity Augmented Diffusion Estimation for Offline Black-Box Optimization
May 11, 2026Yonghan Yang, Ye Yuan, Zipeng Sun +5Surrogate Modeling Surrogate-Assisted Optimization
MBZUAI - Mohamed bin Zayed University of Artificial Intelligence · McGill University · Mila - Quebec AI Institute +1
Rethinking Learnability in Offline Data-driven Optimization
Sep 1, 2026Chao Qian, Chen-Guang Wang, Rong-Xi Tan +1Black-Box Optimization Statistical Learning Theory
State Key Laboratory of Novel Software Technology, Nanjing University, Nanjing 210023, China · School of Artificial Intelligence, Nanjing University, Nanjing 210023, China
On the Learnability of Offline Model-Based Optimization: A Ranking Perspective
Mar 4, 2026Shen-Huan Lyu, Rong-Xi Tan, Ke Xue +4Surrogate Modeling Distribution Shift
Key Laboratory of Water Big Data Technology of Ministry of Water Resources, College of Computer Science and Software Engineering, Hohai University, Nanjing, China · Department of Computer Science, City University of Hong Kong, Hong Kong, China · National Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, China +1

May 11, 2026J/K move · Enter open · S save

Support-Proximity Augmented Diffusion Estimation for Offline Black-Box Optimization

Yonghan Yang, Ye Yuan, Zipeng Sun, Linfeng Du+4

MBZUAI - Mohamed bin Zayed University of Artificial Intelligence · McGill University · Mila - Quebec AI Institute+1

Surrogate Modeling Surrogate-Assisted Optimization Black-Box Optimization OOD Generalization

Open paper AskPDF arXiv

Offline black-box optimization aims to discover novel designs with high property scores using only a static dataset, a task fundamentally challenged by the out-of-distribution (OOD) extrapolation problem. Existing approaches typically bifurcate into inverse methods, which struggle with the ill-posed nature of mapping scores to designs, and forward methods, which often lack the distributional expressivity to quantify uncertainty effectively. In this work, we propose SPADE (Support-Proximity Augmented Diffusion Estimation), a novel framework that reimagines forward surrogate modeling through the lens of conditional generative modeling. SPADE models the forward likelihood p(y|x) using a diffusion model, but with two critical enhancements to tailor it for optimization: (1) a Calibrated Diffusion Estimation module that enforces global consistency in statistical moments and pairwise rankings, and (2) a Support-Proximity Regularization mechanism that implicitly internalizes the data manifold constraint p(x) via kNN-based density estimation. Theoretically, we prove that our regularization is first-order equivalent to maximizing a Bayesian posterior with a valid design prior. Empirically, SPADE achieves state-of-the-art performance across Design-Bench tasks and an LLM data mixture optimization benchmark.

Abstract

Black-Box Optimization

Explore similar work

Support-Proximity Augmented Diffusion Estimation for Offline Black-Box Optimization

Rethinking Learnability in Offline Data-driven Optimization

On the Learnability of Offline Model-Based Optimization: A Ranking Perspective