Using the knowledge gradient acquisition function in Bayesian optimization when searching for robust solutions

This article 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. A variant of the well-known knowledge gradient acquisition function is proposed specifically to search for robust solutions, with analytic expressions for uniformly and normally distributed disturbances. An empirical evaluation on a number of test problems demonstrates that the new acquisition function outperforms alternative approaches.