首次理论分析时变贝叶斯优化的渐近表现，揭示其无悔条件。
Asymptotic Performance of Time-Varying Bayesian Optimization
- 通过上界与下界分析，给出时变贝叶斯优化的累积后悔量级。
- 证明在特定条件下，算法可实现渐近后悔为零。
- 适用于研究动态优化的学者，尤其关注理论保障的工程师。
时变贝叶斯优化（TVBO）是优化随时间变化、噪声且评估代价高的黑箱目标函数的主流框架，但其出色的实验性能尚缺乏理论解释。本文回答了一个关键问题：是否存在一种TVBO算法，使其瞬时后悔在渐近意义上趋于零？我们通过建立累积后悔的上界和算法无关的下界，提供了重要洞察，并推导出具备无悔性质的充分条件。据我们所知，本分析首次覆盖了实际中常用的全部主要平稳核函数类别。
原文摘要 · Abstract (English)
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.
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