Constrained robust Bayesian optimization of expensive noisy black?box functions with guaranteed regret bounds

Many real-world design problems involve optimization of expensive black-box functions. Bayesian (BO) is a promising approach for solving such challenging using probabilistic surrogate models to systematically tradeoff between exploitation and exploration the space. Although BO often applied unconstrained problems, it has recently been extended constrained setting. Current methods, however, cannot identify solutions that are robust unavoidable uncertainties. In this article, we propose method, adversarially (CARBO), addresses challenge by jointly modeling effect variables uncertainties on unknown Using exact penalty functions, establish bound number CARBO iterations required find near-global solution provide rigorous proof convergence. The advantages demonstrated two case studies including non-convex benchmark problem realistic bubble column reactor problem.