Batch Bayesian Optimization via Particle Gradient Flows

Abstract. Bayesian optimization (BO) methods seek to find global optima of objective functions which are only available as a black-box or are expensive to evaluate. Such methods construct a surrogate model for the objective function, quantifying the uncertainty in that surrogate through Bayesian inference. Objective evaluations are sequentially determined by maximizing an acquisition function at each step. However, this ancilliary optimization problem can be highly nontrivial to solve, due to the nonconcavity of the acquisition function, particularly in the case of batch Bayesian optimization, where multiple points are selected in every step. In this work we reformulate batch BO as an optimization problem over the space of probability measures. We construct a new acquisition function based on multipoint expected improvement, which is concave over the space of probability measures. Practical schemes for solving this “inner" optimization problem arise naturally as gradient flows of this objective function. We demonstrate the efficacy of this new method on different benchmark functions and compare with state-of-the-art batch BO methods.