Max-value Entropy Search for Efficient Bayesian Optimization

TL;DR

This paper introduces Max-value Entropy Search (MES), a Bayesian optimization method that reduces computational costs by focusing on the maximum function value, maintaining performance while improving efficiency especially in high-dimensional problems.

Contribution

MES is a novel Bayesian optimization criterion that simplifies entropy estimation by targeting the maximum value, offering theoretical guarantees and improved computational efficiency.

Findings

MES matches or outperforms ES/PES in empirical tests.

MES significantly reduces computational complexity.

MES is more robust in high-dimensional settings.

Abstract

Entropy Search (ES) and Predictive Entropy Search (PES) are popular and empirically successful Bayesian Optimization techniques. Both rely on a compelling information-theoretic motivation, and maximize the information gained about the $\arg\max$ of the unknown function; yet, both are plagued by the expensive computation for estimating entropies. We propose a new criterion, Max-value Entropy Search (MES), that instead uses the information about the maximum function value. We show relations of MES to other Bayesian optimization methods, and establish a regret bound. We observe that MES maintains or improves the good empirical performance of ES/PES, while tremendously lightening the computational burden. In particular, MES is much more robust to the number of samples used for computing the entropy, and hence more efficient for higher dimensional problems.