Bayesian Optimization Searching for Robust Solutions

This paper considers the use of Bayesian optimization to identify robust solutions, where robust means having a high expected performance given disturbances over the decision variables and independent noise in the output. We propose a variant of the well-known Knowledge Gradient acquisition function that has been proposed for the case of optimizing integrals. We empirically evaluate our method on one and two dimensional functions and demonstrate that it significantly outperforms the uniform allocation of sampling points and an alternative approach that estimates each function value by averaging over a random sample.