Maximally Robust Satisficing Bayesian Optimization

2026-07-15

AI Summary

In black-box optimization, the practical objective is often to efficiently identify a satisfactory solution that maintains performance under input perturbations encountered during deployment, rather than pursuing the global optimum. This work proposes a novel Bayesian optimization approach that explicitly distinguishes between controllable and uncontrollable perturbations during the optimization phase, thereby jointly modeling satisficing search and robustness under worst-case disturbances for the first time. By introducing a superlevel-set-oriented robustness metric and designing a corresponding acquisition function, the method efficiently identifies solutions that satisfy a prescribed performance threshold even under maximal perturbations. Empirical results demonstrate that this approach significantly outperforms existing methods that either solely seek optimality or neglect deployment-stage perturbations.

Abstract

Many design tasks can be cast as black-box function optimization, enabling use of Bayesian optimization to find an ideal design with minimal number of trials. However, often we do not actually need the optimum but instead a sufficiently good solution is enough, for instance a material that is durable enough for its intended use. In most cases there are multiple satisfactory solutions, forming a superlevel set of the function, raising a key question of which one to prefer. We answer this by explaining why robustness to input perturbations that may occur when the solution is deployed is a good criterion and by introduce a Bayesian optimization method that efficiently finds satisficing solutions that are robust to maximally large perturbations. In contrast to previous works, we assume the inputs can be accurately controlled during optimization, but will be perturbed after the deployment.

Problem

• satisficing
• robustness
• Bayesian optimization
• input perturbations
• superlevel set

Innovation

• Bayesian optimization
• satisficing
• robustness
• superlevel set
• input perturbations