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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.13012 |
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| _version_ | 1866912660434452480 |
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| author | Bardou, Anthony Thiran, Patrick |
| author_facet | Bardou, Anthony Thiran, Patrick |
| contents | Time-Varying Bayesian Optimization (TVBO) is the go-to framework for optimizing a time-varying black-box objective function that may be noisy and expensive to evaluate, but its excellent empirical performance remains to be understood theoretically. Is it possible for the instantaneous regret of a TVBO algorithm to vanish asymptotically, and if so, when? We answer this question of great importance by providing upper bounds and algorithm-independent lower bounds for the cumulative regret of TVBO algorithms. In doing so, we provide important insights about the TVBO framework and derive sufficient conditions for a TVBO algorithm to have the no-regret property. To the best of our knowledge, our analysis is the first to cover all major classes of stationary kernel functions used in practice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_13012 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotic Performance of Time-Varying Bayesian Optimization Bardou, Anthony Thiran, Patrick Machine Learning Time-Varying Bayesian Optimization (TVBO) is the go-to framework for optimizing a time-varying black-box objective function that may be noisy and expensive to evaluate, but its excellent empirical performance remains to be understood theoretically. Is it possible for the instantaneous regret of a TVBO algorithm to vanish asymptotically, and if so, when? We answer this question of great importance by providing upper bounds and algorithm-independent lower bounds for the cumulative regret of TVBO algorithms. In doing so, we provide important insights about the TVBO framework and derive sufficient conditions for a TVBO algorithm to have the no-regret property. To the best of our knowledge, our analysis is the first to cover all major classes of stationary kernel functions used in practice. |
| title | Asymptotic Performance of Time-Varying Bayesian Optimization |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2505.13012 |