Randomized Gaussian Process Upper Confidence Bound with Tighter Bayesian Regret Bounds

Autor:	Takeno, Shion, Inatsu, Yu, Karasuyama, Masayuki
Rok vydání:	2023
Předmět:	Computer Science - Machine Learning
Druh dokumentu:	Working Paper
Popis:	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. Comment: 33 pages, 3 figures, Accepted to ICML2023
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2302.01511 Zobrazit plný text záznamu View this record from Arxiv