Bayesian Optimization for Distributionally Robust Chance-constrained Problem

Under the presence of these two types of variables, the goal is to identify the design variables that optimize the black-box function by taking into account the uncertainty of environmental variables. In the past few years, Bayesian Optimization (BO) framework that takes the uncertain environmental variables into considerations have been studied in various setups (see §1.1). In this paper, we study one of such problems called distributionally robust chance-constrained (DRCC) problem. The DRCC problem is an instance of constrained optimization problems in an uncertain environment, which is important in a variety of practical problems in science and engineering. The goal of a CC problem is to identify the design variables that maximize the expectation of the objective function under the constraint that the probability of the constraint function exceeding a given threshold is greater than a certain level. Let f(x, w) and g(x, w) be the unknown objective and constraint functions, respectively, both of which depend on the design variables x X and the environmental variables w Ω.