Exploring Exploration in Bayesian Optimization

Leonard Papenmeier, Nuojin Cheng, Stephen Becker, Luigi Nardi
Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence, PMLR 286:3388-3415, 2025.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v286-papenmeier25a, title = {Exploring Exploration in Bayesian Optimization}, author = {Papenmeier, Leonard and Cheng, Nuojin and Becker, Stephen and Nardi, Luigi}, booktitle = {Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence}, pages = {3388--3415}, year = {2025}, editor = {Chiappa, Silvia and Magliacane, Sara}, volume = {286}, series = {Proceedings of Machine Learning Research}, month = {21--25 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v286/main/assets/papenmeier25a/papenmeier25a.pdf}, url = {https://proceedings.mlr.press/v286/papenmeier25a.html}, 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.} }
Endnote
%0 Conference Paper %T Exploring Exploration in Bayesian Optimization %A Leonard Papenmeier %A Nuojin Cheng %A Stephen Becker %A Luigi Nardi %B Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2025 %E Silvia Chiappa %E Sara Magliacane %F pmlr-v286-papenmeier25a %I PMLR %P 3388--3415 %U https://proceedings.mlr.press/v286/papenmeier25a.html %V 286 %X 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.
APA
Papenmeier, L., Cheng, N., Becker, S. & Nardi, L.. (2025). Exploring Exploration in Bayesian Optimization. Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 286:3388-3415 Available from https://proceedings.mlr.press/v286/papenmeier25a.html.

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