Maximally Robust Satisficing Bayesian Optimization

Many design tasks can be cast as black-box function optimization, enabling use of Bayesian optimization to find an ideal design with minimal number of trials. However, often we do not actually need the optimum but instead a sufficiently good solution is enough, for instance a material that is durable enough for its intended use. In most cases there are multiple satisfactory solutions, forming a superlevel set of the function, raising a key question of which one to prefer. We answer this by explaining why robustness to input perturbations that may occur when the solution is deployed is a good criterion and by introduce a Bayesian optimization method that efficiently finds satisficing solutions that are robust to maximally large perturbations. In contrast to previous works, we assume the inputs can be accurately controlled during optimization, but will be perturbed after the deployment.