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Boosting Offline Optimizers with Surrogate Sensitivity

Manh Cuong Dao, Phi Le Nguyen, Thao Nguyen Truong, Trong Nghia Hoang

TL;DR

This work tackles offline optimization by introducing a model-agnostic sensitivity measure for surrogates and a corresponding sensitivity-informed regularizer (BOSS) to improve existing offline optimizers. By formulating a minimax objective that minimizes surrogate loss while maximizing worst-case sensitivity, BOSS encourages more robust predictions in out-of-distribution regions visited during optimization. Empirical results on six Design-Bench tasks show consistent performance boosts across 11 baselines, with notable gains and reduced variance, and ablations validate the stability of key hyperparameters. The approach is modular and can synergistically enhance a wide range of offline optimization workflows, with potential extensions to safe BO and safe RL.

Abstract

Offline optimization is an important task in numerous material engineering domains where online experimentation to collect data is too expensive and needs to be replaced by an in silico maximization of a surrogate of the black-box function. Although such a surrogate can be learned from offline data, its prediction might not be reliable outside the offline data regime, which happens when the surrogate has narrow prediction margin and is (therefore) sensitive to small perturbations of its parameterization. This raises the following questions: (1) how to regulate the sensitivity of a surrogate model; and (2) whether conditioning an offline optimizer with such less sensitive surrogate will lead to better optimization performance. To address these questions, we develop an optimizable sensitivity measurement for the surrogate model, which then inspires a sensitivity-informed regularizer that is applicable to a wide range of offline optimizers. This development is both orthogonal and synergistic to prior research on offline optimization, which is demonstrated in our extensive experiment benchmark.

Boosting Offline Optimizers with Surrogate Sensitivity

TL;DR

This work tackles offline optimization by introducing a model-agnostic sensitivity measure for surrogates and a corresponding sensitivity-informed regularizer (BOSS) to improve existing offline optimizers. By formulating a minimax objective that minimizes surrogate loss while maximizing worst-case sensitivity, BOSS encourages more robust predictions in out-of-distribution regions visited during optimization. Empirical results on six Design-Bench tasks show consistent performance boosts across 11 baselines, with notable gains and reduced variance, and ablations validate the stability of key hyperparameters. The approach is modular and can synergistically enhance a wide range of offline optimization workflows, with potential extensions to safe BO and safe RL.

Abstract

Offline optimization is an important task in numerous material engineering domains where online experimentation to collect data is too expensive and needs to be replaced by an in silico maximization of a surrogate of the black-box function. Although such a surrogate can be learned from offline data, its prediction might not be reliable outside the offline data regime, which happens when the surrogate has narrow prediction margin and is (therefore) sensitive to small perturbations of its parameterization. This raises the following questions: (1) how to regulate the sensitivity of a surrogate model; and (2) whether conditioning an offline optimizer with such less sensitive surrogate will lead to better optimization performance. To address these questions, we develop an optimizable sensitivity measurement for the surrogate model, which then inspires a sensitivity-informed regularizer that is applicable to a wide range of offline optimizers. This development is both orthogonal and synergistic to prior research on offline optimization, which is demonstrated in our extensive experiment benchmark.

Paper Structure

This paper contains 28 sections, 2 theorems, 27 equations, 7 figures, 7 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Sensitivity-Guided Offline Optimization
  4. Problem Setting and Notations
  5. Sensitivity of Surrogate Model
  6. Sensitivity-Informed Regularizer
  7. Practical Algorithm
  8. Experiments
  9. Benchmarks, Baselines and Evaluation
  10. Results and Discussion
  11. Ablation Experiments
  12. Conclusion
  13. Derivation of Lemma \ref{['lem:1']}
  14. Derivation of Lemma \ref{['lem:2']}
  15. Alternative Formulation of BOSS : BOSS-2 via using Taylor Approximation in Eq. \ref{['eq:8']}
  16. ...and 13 more sections

Key Result

Lemma 3.2

Let $\mathcal{S}_\phi(\alpha, \omega)$ defined via Definition def:1. Suppose $\mathcal{S}_\phi(\alpha, \omega) \geq 1 - \delta$ with $\delta \in (0, 1)$. Then, with probability at least $1 - \delta$ over the space of random perturbation $\gamma \sim \mathbb{N}(\omega_\mu, \omega_\sigma^2\mathbf{I})$ where $\mathfrak{L}_\phi \triangleq \max_\gamma \mathfrak{L}_{\phi + \gamma}$ and $\mathfrak{L}_{\p

Figures (7)

  • Figure 1: Workflows of (a) existing offline optimizers; and (b) our sensitivity-informed regularized optimizer (BOSS) which regulates the training workflow of existing offline optimizers with a new sensitivity metric -- see Definition \ref{['def:1']}. Our regularizer is generic and can be applied to most existing offline optimizer workflows to boost their performance as demonstrated in Section \ref{['sec:experiment']}.
  • Figure 2: Plots of performance variation of COMS and GA (regularized by BOSS) to changes in (a) the no. of gradient ascent steps during optimization; (b) values of the sensitivity threshold $\alpha$; (c) changes in the no. of perturbation samples $m$; and (d) changes in value ranges of bound $([\omega_{\mu_l},\omega_{\mu_u}],[\omega_{\sigma_l},\omega_{\sigma_u}])$ for parameter $\omega$ of the perturbation distribution. These are $([-10^{-3},10^{-3}],[10^{-5},10^{-2}])$, $([-10^{-3},10^{-3}],[10^{-6},10^{-3}])$, $([-10^{-2},10^{-2}],[10^{-5},10^{-2}])$, and $([-10^{-2},10^{-2}],[10^{-6},10^{-3}])$ which are indexed with 0, 1, 2, 3 in this figure.
  • Figure 3: The mean and standard deviation of $|S_\phi-S_\phi^+|$ across data batches during 50 epochs of GA on Superconductor and TF-BIND-8.
  • Figure 4: Improvement in terms of RMSE and correlation between the final performance with RMSE of CBAS, COMs on unseen data after being conditioned with BOSS on TF-BIND-8 and TF-BIND-10.
  • Figure 5: Additional experiments: (a) Comparison BOSS with $L1$ and $L2$ regularization; (b) Root-mean-square-error (RMSE) of surrogate model trained with and without BOSS in simulated out-of-distribution regime.
  • ...and 2 more figures

Theorems & Definitions (3)

  • Definition 3.1
  • Lemma 3.2
  • Lemma 4.1