Bayesian Optimization for Distributionally Robust Chance-constrained Problem

TL;DR

This paper introduces a Bayesian optimization approach for distributionally robust chance-constrained problems, effectively handling uncertainty in environmental variables without precise distribution knowledge, and demonstrates its high accuracy and practical usefulness.

Contribution

It proposes a novel DRCC Bayesian optimization method that works without exact environmental distribution information, ensuring high-probability solution accuracy.

Findings

Method achieves arbitrarily accurate solutions with high probability

Numerical experiments confirm the method's effectiveness

Handles uncertainty in environmental variables without precise distribution knowledge

Abstract

In black-box function optimization, we need to consider not only controllable design variables but also uncontrollable stochastic environment variables. In such cases, it is necessary to solve the optimization problem by taking into account the uncertainty of the environmental variables. Chance-constrained (CC) problem, the problem of maximizing the expected value under a certain level of constraint satisfaction probability, is one of the practically important problems in the presence of environmental variables. In this study, we consider distributionally robust CC (DRCC) problem and propose a novel DRCC Bayesian optimization method for the case where the distribution of the environmental variables cannot be precisely specified. We show that the proposed method can find an arbitrary accurate solution with high probability in a finite number of trials, and confirm the usefulness of the proposed method through numerical experiments.