A Lipschitz exploration-exploitation scheme for Bayesian optimization

Abstract

The problem of optimizing unknown costly-to-evaluate functions has been studied extensively in the context of Bayesian optimization. Algorithms in this field aim to find the optimizer of the function by requesting only a few function evaluations at carefully selected locations. An ideal algorithm should maintain a perfect balance between exploration (probing unexplored areas) and exploitation (focusing on promising areas) within the given evaluation budget. In this paper, we assume the unknown function is Lipschitz continuous. Leveraging the Lipschitz property, we propose an algorithm with a distinct exploration phase followed by an exploitation phase. The exploration phase aims to select samples that shrink the search space as much as possible, while the exploitation phase focuses on the reduced search space and selects samples closest to the optimizer. We empirically show that the proposed algorithm significantly outperforms the baseline algorithms. © 2013 Springer-Verlag.