arXiv：cs.LG· Anthony Bardou, Patrick Thiran·· 5 小时前AI 评分32
时变贝叶斯优化（TVBO）的渐近性能分析
Asymptotic Performance of Time-Varying Bayesian Optimization
AI 导读
研究首次为时变贝叶斯优化（TVBO）算法的累积遗憾给出上界与算法无关的下界，并推导出TVBO算法具备无遗憾（no-regret）性质的充分条件，回答了瞬时遗憾能否渐近消失的问题。该分析首次覆盖实践中所有主要类别的平稳核函数。
正文
Abstract: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.
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG) |
| Cite as: | arXiv:2505.13012 [stat.ML] |
| (or arXiv:2505.13012v3 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2505.13012 arXiv-issued DOI via DataCite |
Submission history
From: Anthony Bardou [view email]
[v1]
Mon, 19 May 2025 11:55:02 UTC (415 KB)
[v2]
Mon, 20 Oct 2025 15:31:34 UTC (460 KB)
[v3]
Fri, 2 Oct 2026 07:47:52 UTC (786 KB)
来源：arXiv：cs.LG · arxiv.org