Posterior Sampling-Based Bayesian Optimization with Tighter Bayesian Regret Bounds
| Title: | Posterior Sampling-Based Bayesian Optimization with Tighter Bayesian Regret Bounds |
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| Authors: | Takeno, Shion, Inatsu, Yu, Karasuyama, Masayuki, Takeuchi, Ichiro |
| Publication Year: | 2023 |
| Collection: | Computer Science Statistics |
| Subject Terms: | Computer Science - Machine Learning, Statistics - Machine Learning |
| More Details: | 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. Comment: 28 pages, 3 figures, 2 tables, Accepted to ICML2024 |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/2311.03760 |
| Accession Number: | edsarx.2311.03760 |
| Database: | arXiv |
| Description not available. |