A Lipschitz Exploration-Exploitation Scheme for Bayesian Optimization

TL;DR

This paper introduces a novel Bayesian optimization algorithm that leverages Lipschitz continuity to efficiently explore and exploit the search space, outperforming traditional Expected Improvement methods.

Contribution

The paper proposes a Lipschitz-based exploration-exploitation scheme that improves search efficiency in Bayesian optimization by reducing the search space before exploitation.

Findings

The proposed algorithm outperforms Expected Improvement in empirical tests.

Lipschitz property effectively guides exploration to shrink the search space.

The method achieves faster convergence with fewer function evaluations.

Abstract

The problem of optimizing unknown costly-to-evaluate functions has been studied for a long time in the context of Bayesian Optimization. Algorithms in this field aim to find the optimizer of the function by asking only a few function evaluations at locations carefully selected based on a posterior model. 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. The exploitation phase then focuses on the reduced search space and selects samples closest to the optimizer. Considering the Expected Improvement (EI) as a baseline, we empirically show that the proposed algorithm significantly outperforms EI.