Exploring Exploration in Bayesian Optimization

Leonard Papenmeier, Nuojin Cheng, Stephen Becker, Luigi Nardi

Keywords: Bayesian Optimization, Acquisition Functions, Black-Box Optimization, Gaussian Processes, Uncertainty Quantification, Global Optimization

TL;DR: The paper introduces two novel metrics, Observation Traveling Salesman Distance and Observation Entropy, to quantify exploration in Bayesian optimization, enabling systematic analysis of acquisition functions and their exploration.

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.

Code Link: https://github.com/LeoIV/exploring-exploration-public

Readers: auai.org/UAI/2025/Conference, auai.org/UAI/2025/Conference/Area_Chairs, auai.org/UAI/2025/Conference/Reviewers, auai.org/UAI/2025/Conference/Submission798/Authors, auai.org/UAI/2025/Conference/Submission798/Reproducibility_Reviewers

Submission Number: 798