Exploring Exploration in Bayesian Optimization

TL;DR

This paper introduces two new quantitative measures to analyze and compare the exploration behavior of acquisition functions in Bayesian optimization, enhancing understanding and guiding their design.

Contribution

It proposes observation traveling salesman distance and observation entropy as novel metrics for exploration, and applies them to analyze various acquisition functions.

Findings

New measures reveal links between exploration and performance.

Analysis uncovers relationships among existing acquisition functions.

Metrics enable principled design of acquisition functions.

Abstract

A well-balanced exploration-exploitation trade-off is crucial for successful acquisition functions in Bayesian optimization. However, there is a lack of quantitative measures for exploration, making it difficult to analyze and compare different acquisition functions. This work introduces two novel approaches - observation traveling salesman distance and observation entropy - to quantify the exploration characteristics of acquisition functions based on their selected observations. Using these measures, we examine the explorative nature of several well-known acquisition functions across a diverse set of black-box problems, uncover links between exploration and empirical performance, and reveal new relationships among existing acquisition functions. Beyond enabling a deeper understanding of acquisition functions, these measures also provide a foundation for guiding their design in a more principled and systematic manner.