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.

翻译：在黑箱功能优化中,我们不仅需要考虑可控的设计变量,还需要考虑不可控的随机环境变量。在这种情况下,有必要通过考虑到环境变量的不确定性来解决优化问题。受时间限制(CC)的问题,即在一定的制约性满意度水平下实现预期价值最大化的问题,是环境变量存在的实际重要问题之一。在本研究中,我们认为分布性强的CC(DRCC)问题,并为环境变量分布无法精确指定的情况下提出了新的TRDCC Bayesian优化方法。我们表明,拟议方法可以找到任意准确的解决办法,在一定数量的试验中极有可能找到,并通过数字实验确认拟议方法的有用性。