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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

TL;DR

This work argues that offline optimization is fundamentally a problem of ranking high-quality designs rather than accurate value prediction, and introduces an optimization-oriented risk based on ranking between near-optimal and suboptimal designs, and develops a unified theoretical framework that connects surrogate learning to final optimization.

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.

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

TL;DR

This work argues that offline optimization is fundamentally a problem of ranking high-quality designs rather than accurate value prediction, and introduces an optimization-oriented risk based on ranking between near-optimal and suboptimal designs, and develops a unified theoretical framework that connects surrogate learning to final optimization.

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.
Paper Structure (38 sections, 9 theorems, 108 equations, 2 figures, 4 tables, 1 algorithm)

This paper contains 38 sections, 9 theorems, 108 equations, 2 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Problem setting:
  4. Surrogate learning:
  5. Optimization:
  6. Theoretical Results
  7. Learnability of Rank-based Offline MBO
  8. Ranking is Better than Regression
  9. Distribution Shift and Algorithmic Inspiration
  10. Geometric Separation of Offline MBO
  11. Distribution-Aware Ranking (DAR)
  12. Motivation.
  13. Dataset construction.
  14. Ranking loss learning.
  15. Optimization adaptation.
  16. ...and 23 more sections

Key Result

Lemma 4

Let $\{({\boldsymbol{x}}_i,{\boldsymbol{x}}_j')| (i,j)\in [m]^2\}$ be training pairs induced by the dataset $S$ draw from the training distribution $Q_{\mathrm{tr}}$ and $\mathcal{F} := \bigl\{ ({\boldsymbol{x}},{\boldsymbol{x}}') \mapsto \ell_{\mathrm{rank}}(h_\theta;{\boldsymbol{x}},{\boldsymbol{x

Figures (2)

  • 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.

Theorems & Definitions (16)

  • Definition 1
  • Definition 2
  • Definition 3
  • Lemma 4
  • Theorem 5
  • Remark 1
  • Lemma 6
  • Theorem 7
  • Remark 2
  • Lemma 8
  • ...and 6 more