Posterior Sampling-Based Bayesian Optimization with Tighter Bayesian Regret Bounds

Shion Takeno, Yu Inatsu, Masayuki Karasuyama, Ichiro Takeuchi
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:47510-47534, 2024.

Abstract

Among various acquisition functions (AFs) in Bayesian optimization (BO), Gaussian process upper confidence bound (GP-UCB) and Thompson sampling (TS) are well-known options with established theoretical properties regarding Bayesian cumulative regret (BCR). Recently, it has been shown that a randomized variant of GP-UCB achieves a tighter BCR bound compared with GP-UCB, which we call the tighter BCR bound for brevity. Inspired by this study, this paper first shows that TS achieves the tighter BCR bound. On the other hand, GP-UCB and TS often practically suffer from manual hyperparameter tuning and over-exploration issues, respectively. Therefore, we analyze yet another AF called a probability of improvement from the maximum of a sample path (PIMS). We show that PIMS achieves the tighter BCR bound and avoids the hyperparameter tuning, unlike GP-UCB. Furthermore, we demonstrate a wide range of experiments, focusing on the effectiveness of PIMS that mitigates the practical issues of GP-UCB and TS.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-takeno24a, title = {Posterior Sampling-Based {B}ayesian Optimization with Tighter {B}ayesian Regret Bounds}, author = {Takeno, Shion and Inatsu, Yu and Karasuyama, Masayuki and Takeuchi, Ichiro}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {47510--47534}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/takeno24a/takeno24a.pdf}, url = {https://proceedings.mlr.press/v235/takeno24a.html}, abstract = {Among various acquisition functions (AFs) in Bayesian optimization (BO), Gaussian process upper confidence bound (GP-UCB) and Thompson sampling (TS) are well-known options with established theoretical properties regarding Bayesian cumulative regret (BCR). Recently, it has been shown that a randomized variant of GP-UCB achieves a tighter BCR bound compared with GP-UCB, which we call the tighter BCR bound for brevity. Inspired by this study, this paper first shows that TS achieves the tighter BCR bound. On the other hand, GP-UCB and TS often practically suffer from manual hyperparameter tuning and over-exploration issues, respectively. Therefore, we analyze yet another AF called a probability of improvement from the maximum of a sample path (PIMS). We show that PIMS achieves the tighter BCR bound and avoids the hyperparameter tuning, unlike GP-UCB. Furthermore, we demonstrate a wide range of experiments, focusing on the effectiveness of PIMS that mitigates the practical issues of GP-UCB and TS.} }
Endnote
%0 Conference Paper %T Posterior Sampling-Based Bayesian Optimization with Tighter Bayesian Regret Bounds %A Shion Takeno %A Yu Inatsu %A Masayuki Karasuyama %A Ichiro Takeuchi %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-takeno24a %I PMLR %P 47510--47534 %U https://proceedings.mlr.press/v235/takeno24a.html %V 235 %X Among various acquisition functions (AFs) in Bayesian optimization (BO), Gaussian process upper confidence bound (GP-UCB) and Thompson sampling (TS) are well-known options with established theoretical properties regarding Bayesian cumulative regret (BCR). Recently, it has been shown that a randomized variant of GP-UCB achieves a tighter BCR bound compared with GP-UCB, which we call the tighter BCR bound for brevity. Inspired by this study, this paper first shows that TS achieves the tighter BCR bound. On the other hand, GP-UCB and TS often practically suffer from manual hyperparameter tuning and over-exploration issues, respectively. Therefore, we analyze yet another AF called a probability of improvement from the maximum of a sample path (PIMS). We show that PIMS achieves the tighter BCR bound and avoids the hyperparameter tuning, unlike GP-UCB. Furthermore, we demonstrate a wide range of experiments, focusing on the effectiveness of PIMS that mitigates the practical issues of GP-UCB and TS.
APA
Takeno, S., Inatsu, Y., Karasuyama, M. & Takeuchi, I.. (2024). Posterior Sampling-Based Bayesian Optimization with Tighter Bayesian Regret Bounds. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:47510-47534 Available from https://proceedings.mlr.press/v235/takeno24a.html.

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