Bayesian Optimization for Distributionally Robust Chance-constrained Problem
This addresses uncertainty in environmental variables for optimization practitioners, but it is incremental as it builds on existing chance-constrained and Bayesian optimization frameworks.
The authors tackled the distributionally robust chance-constrained (DRCC) problem in black-box optimization with uncontrollable stochastic variables, proposing a novel Bayesian optimization method that finds arbitrarily accurate solutions with high probability in finite trials, as confirmed through numerical experiments.
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.