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

Shen-Huan Lyu; Rong-Xi Tan; Ke Xue; Yi-Xiao He; Yu Huang; Qingfu Zhang; Chao Qian

cs.LGMar 4, 2026

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

Authors: Shen-Huan Lyu, Rong-Xi Tan, Ke Xue, Yi-Xiao He, Yu Huang, Qingfu Zhang, Chao Qian

Organizations: 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 · School of Artificial Intelligence and Information Technology, Nanjing University of Chinese Medicine, Nanjing, China

Abstract

Offline model-based optimization (MBO) seeks to discover high-performing designs using only a fixed dataset of past evaluations. Most existing methods rely on learning a surrogate model via regression and implicitly assume that good predictive accuracy leads to good optimization performance. In this work, we challenge this assumption and study offline MBO from a learnability perspective. We argue that offline optimization is fundamentally a problem of ranking high-quality designs rather than accurate value prediction. Specifically, we introduce an optimization-oriented risk based on ranking between near-optimal and suboptimal designs, and develop a unified theoretical framework that connects surrogate learning to final optimization. We prove the theoretical advantages of ranking over regression, and identify distributional mismatch between the training data and near-optimal designs as the dominant error. Inspired by this, we design a distribution-aware ranking method to reduce this mismatch. Empirical results across various tasks show that our approach outperforms twenty existing methods, validating our theoretical findings. Additionally, both theoretical and empirical results reveal intrinsic limitations in offline MBO, showing a regime in which no offline method can avoid over-optimistic extrapolation.

Figures & tables

Panel of Figure 1 — Figure 1: Landscape analysis on the Branin function. (a) The landscape of the Branin function and the distribution of the offline dataset (black dots), which consists of the worst 60% of designs. (b) and (c) present the prediction landscape derived from the MSE-trained surrogate and DAR-trained surrogate, respectively. The DAR surrogate accurately extrapolates the landscape structure, recovering the three distinct peaks of the true optima with high fidelity, whereas the MSE baseline fails to precisely recover these modes.

Figure 2: Comparison of surrogates trained with MSE, RaM, and DAR on optimization-oriented ranking error.

Method	Ant	D’Kitty	Superconductor	TF-Bind-8	TF-Bind-10	Avg. Rank
$S$ (best)	0.565	0.884	0.400	0.439	0.467	/
PGS ( Chemingui et al., 2024 )	0.715 ± 0.046	0.954 ± 0.022	0.444 ± 0.020	0.889 ± 0.061	0.634 ± 0.040	5.4
FGM ( Grudzien et al., 2024 )	0.923 ± 0.023	0.944 ± 0.014	0.481 ± 0.024	0.811 ± 0.079	0.611 ± 0.008	5.8
Match-OPT ( Hoang et al., 2024 )	0.933 ± 0.016	0.952 ± 0.008	0.504 ± 0.021	0.824 ± 0.067	0.655 ± 0.050	4.0
GTG ( Yun et al., 2024 )	0.855 ± 0.044	0.942 ± 0.017	0.480 ± 0.055	0.910 ± 0.040	0.619 ± 0.029	5.6
RaM ( Tan et al., 2025 )	0.940 ± 0.028	0.951 ± 0.017	0.514 ± 0.026	0.982 ± 0.012	0.675 ± 0.049	2.6

Table 1: 100th percentile normalized score in Design-Bench, where the best and runner-up results on each task are Blue and Violet .

S

(best) denotes the best score in the offline dataset. Results of compared methods are either inherited from Tan et al. (2025) or run by us.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

$\lambda$	Ant	D’Kitty	Superconductor	TF-Bind-8	TF-Bind-10	Avg. Rank
0.0	0.900 $\pm$ 0.032	0.950 $\pm$ 0.012	0.496 $\pm$ 0.009	0.989 $\pm$ 0.003	0.670 $\pm$ 0.069	3.4
0.1	0.941 $\pm$ 0.013	0.959 $\pm$ 0.006	0.506 $\pm$ 0.008	0.988 $\pm$ 0.008	0.686 $\pm$ 0.056	1.6
0.2	0.914 $\pm$ 0.032	0.949 $\pm$ 0.007	0.507 $\pm$ 0.009	0.979 $\pm$ 0.019	0.674 $\pm$ 0.058	3.4
0.3	0.923 $\pm$ 0.024	0.946 $\pm$ 0.006	0.496 $\pm$ 0.029	0.984 $\pm$ 0.008	0.647 $\pm$ 0.036	3.6
0.4	0.919 $\pm$ 0.013	0.943 $\pm$ 0.005	0.476 $\pm$ 0.047	0.978 $\pm$ 0.014	0.642 $\pm$ 0.035	5.4
0.5	0.937 $\pm$ 0.018	0.943 $\pm$ 0.005	0.473 $\pm$ 0.050	0.981 $\pm$ 0.008	0.699 $\pm$ 0.096	3.6

Appendix

Table 2: Ablation study on interpolation coefficient

\lambda

$\beta$	Ant	D’Kitty	Superconductor	TF-Bind-8	TF-Bind-10	Avg. Rank
0.0	0.936 $\pm$ 0.025	0.960 $\pm$ 0.011	0.505 $\pm$ 0.008	0.982 $\pm$ 0.015	0.672 $\pm$ 0.060	2.4
0.1	0.919 $\pm$ 0.036	0.951 $\pm$ 0.008	0.498 $\pm$ 0.011	0.975 $\pm$ 0.017	0.640 $\pm$ 0.045	5.6
0.2	0.920 $\pm$ 0.022	0.953 $\pm$ 0.010	0.504 $\pm$ 0.005	0.983 $\pm$ 0.010	0.641 $\pm$ 0.029	3.8
0.3	0.927 $\pm$ 0.022	0.952 $\pm$ 0.008	0.503 $\pm$ 0.007	0.987 $\pm$ 0.004	0.659 $\pm$ 0.025	3.6
0.4	0.941 $\pm$ 0.013	0.959 $\pm$ 0.006	0.506 $\pm$ 0.008	0.988 $\pm$ 0.008	0.686 $\pm$ 0.056	1.2
0.5	0.931 $\pm$ 0.012	0.948 $\pm$ 0.005	0.503 $\pm$ 0.006	0.983 $\pm$ 0.016	0.634 $\pm$ 0.028	4.4

Appendix

Table 3: Ablation study on margin

\beta

$\varepsilon$	Ant	D’Kitty	Superconductor	TF-Bind-8	TF-Bind-10	Avg. Rank
0.05	0.924 $\pm$ 0.015	0.944 $\pm$ 0.006	0.405 $\pm$ 0.037	0.941 $\pm$ 0.018	0.654 $\pm$ 0.029	4.6
0.1	0.930 $\pm$ 0.012	0.942 $\pm$ 0.008	0.498 $\pm$ 0.012	0.961 $\pm$ 0.033	0.674 $\pm$ 0.054	4.0
0.15	0.931 $\pm$ 0.021	0.946 $\pm$ 0.007	0.505 $\pm$ 0.011	0.973 $\pm$ 0.021	0.674 $\pm$ 0.055	2.6
0.2	0.941 $\pm$ 0.013	0.959 $\pm$ 0.006	0.506 $\pm$ 0.008	0.988 $\pm$ 0.008	0.686 $\pm$ 0.056	1.4
0.25	0.912 $\pm$ 0.018	0.959 $\pm$ 0.008	0.503 $\pm$ 0.009	0.978 $\pm$ 0.013	0.689 $\pm$ 0.155	2.4

Appendix

Table 4: Ablation study on positive ratio

\varepsilon

Surrogate Modeling

Surrogate modeling builds faster or more interpretable approximations of expensive simulations and black-box models.

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Rethinking Learnability in Offline Data-driven Optimization

Chao Qian, Chen-Guang Wang, Rong-Xi Tan, Ke Xue

State Key Laboratory of Novel Software Technology, Nanjing University, Nanjing 210023, China · School of Artificial Intelligence, Nanjing University, Nanjing 210023, China

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Black-Box Optimization (BBO) has broad applications, while traditional algorithms such as evolutionary algorithms and Bayesian optimization face efficiency challenges as real-world BBO problems grow increasingly complex. Data-driven optimization has been the most popular paradigm to improve the efficiency of BBO, by learning from data. Offline data-driven optimization seeks high-quality solutions using only a fixed set of previous evaluations, attracting substantial attention because it requires no additional online evaluations. Many offline optimization methods have been proposed, but a fundamental question remains unanswered: what learnability is sufficient for offline optimization? Prior theoretical studies show that Probably Approximately Correct (PAC) learnability is insufficient, as the optimal region may remain poorly learned even when most regions are well learned. In this paper, we propose algorithm-dependent learnability, which requires accuracy only on the optimizer's trajectory. We prove that its value-query form is sufficient for representative discrete settings, including greedy and local search for submodular maximization, while its first-order analogue is sufficient for projected gradient descent on convex minimization. Motivated by this notion, we formalize a trajectory-learning framework comprising trajectory construction, trajectory modeling, and candidate generation, and analyze existing trajectory-based methods under it. We further propose Uncertainty-aware Gradient-guided Trajectory Learning (UGTL), which constructs locally coherent improvement trajectories reflecting plausible search paths, models them with conditional diffusion, and selects a diverse candidate set. Our experiments show that UGTL achieves the best average rank, 3.1/25, among 25 methods on Design-Bench tasks, and confirm that our trajectory construction plays a significant role in the improvement.

Abstract

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