Regret Analysis of Posterior Sampling-Based Expected Improvement for Bayesian Optimization
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914066064211968 |
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| author | Takeno, Shion Inatsu, Yu Karasuyama, Masayuki Takeuchi, Ichiro |
| author_facet | Takeno, Shion Inatsu, Yu Karasuyama, Masayuki Takeuchi, Ichiro |
| contents | Bayesian optimization is a powerful tool for optimizing an expensive-to-evaluate black-box function. In particular, the effectiveness of expected improvement (EI) has been demonstrated in a wide range of applications. However, theoretical analyses of EI are limited compared with other theoretically established algorithms. This paper analyzes a randomized variant of EI, which evaluates the EI from the maximum of the posterior sample path. We show that this posterior sampling-based random EI achieves the sublinear Bayesian cumulative regret bounds under the assumption that the black-box function follows a Gaussian process. Finally, we demonstrate the effectiveness of the proposed method through numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09828 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regret Analysis of Posterior Sampling-Based Expected Improvement for Bayesian Optimization Takeno, Shion Inatsu, Yu Karasuyama, Masayuki Takeuchi, Ichiro Machine Learning Bayesian optimization is a powerful tool for optimizing an expensive-to-evaluate black-box function. In particular, the effectiveness of expected improvement (EI) has been demonstrated in a wide range of applications. However, theoretical analyses of EI are limited compared with other theoretically established algorithms. This paper analyzes a randomized variant of EI, which evaluates the EI from the maximum of the posterior sample path. We show that this posterior sampling-based random EI achieves the sublinear Bayesian cumulative regret bounds under the assumption that the black-box function follows a Gaussian process. Finally, we demonstrate the effectiveness of the proposed method through numerical experiments. |
| title | Regret Analysis of Posterior Sampling-Based Expected Improvement for Bayesian Optimization |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2507.09828 |