Randomized Gaussian Process Upper Confidence Bound with Tighter Bayesian Regret Bounds

Shion Takeno, Yu Inatsu, Masayuki Karasuyama
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:33490-33515, 2023.

Abstract

Gaussian process upper confidence bound (GP-UCB) is a theoretically promising approach for black-box optimization; however, the confidence parameter $\beta$ is considerably large in the theorem and chosen heuristically in practice. Then, randomized GP-UCB (RGP-UCB) uses a randomized confidence parameter, which follows the Gamma distribution, to mitigate the impact of manually specifying $\beta$. This study first generalizes the regret analysis of RGP-UCB to a wider class of distributions, including the Gamma distribution. Furthermore, we propose improved RGP-UCB (IRGP-UCB) based on a two-parameter exponential distribution, which achieves tighter Bayesian regret bounds. IRGP-UCB does not require an increase in the confidence parameter in terms of the number of iterations, which avoids over-exploration in the later iterations. Finally, we demonstrate the effectiveness of IRGP-UCB through extensive experiments.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-takeno23a, title = {Randomized {G}aussian Process Upper Confidence Bound with Tighter {B}ayesian Regret Bounds}, author = {Takeno, Shion and Inatsu, Yu and Karasuyama, Masayuki}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {33490--33515}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/takeno23a/takeno23a.pdf}, url = {https://proceedings.mlr.press/v202/takeno23a.html}, abstract = {Gaussian process upper confidence bound (GP-UCB) is a theoretically promising approach for black-box optimization; however, the confidence parameter $\beta$ is considerably large in the theorem and chosen heuristically in practice. Then, randomized GP-UCB (RGP-UCB) uses a randomized confidence parameter, which follows the Gamma distribution, to mitigate the impact of manually specifying $\beta$. This study first generalizes the regret analysis of RGP-UCB to a wider class of distributions, including the Gamma distribution. Furthermore, we propose improved RGP-UCB (IRGP-UCB) based on a two-parameter exponential distribution, which achieves tighter Bayesian regret bounds. IRGP-UCB does not require an increase in the confidence parameter in terms of the number of iterations, which avoids over-exploration in the later iterations. Finally, we demonstrate the effectiveness of IRGP-UCB through extensive experiments.} }
Endnote
%0 Conference Paper %T Randomized Gaussian Process Upper Confidence Bound with Tighter Bayesian Regret Bounds %A Shion Takeno %A Yu Inatsu %A Masayuki Karasuyama %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-takeno23a %I PMLR %P 33490--33515 %U https://proceedings.mlr.press/v202/takeno23a.html %V 202 %X Gaussian process upper confidence bound (GP-UCB) is a theoretically promising approach for black-box optimization; however, the confidence parameter $\beta$ is considerably large in the theorem and chosen heuristically in practice. Then, randomized GP-UCB (RGP-UCB) uses a randomized confidence parameter, which follows the Gamma distribution, to mitigate the impact of manually specifying $\beta$. This study first generalizes the regret analysis of RGP-UCB to a wider class of distributions, including the Gamma distribution. Furthermore, we propose improved RGP-UCB (IRGP-UCB) based on a two-parameter exponential distribution, which achieves tighter Bayesian regret bounds. IRGP-UCB does not require an increase in the confidence parameter in terms of the number of iterations, which avoids over-exploration in the later iterations. Finally, we demonstrate the effectiveness of IRGP-UCB through extensive experiments.
APA
Takeno, S., Inatsu, Y. & Karasuyama, M.. (2023). Randomized Gaussian Process Upper Confidence Bound with Tighter Bayesian Regret Bounds. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:33490-33515 Available from https://proceedings.mlr.press/v202/takeno23a.html.

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