Asymptotic Performance of Time-Varying Bayesian Optimization

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.

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2505.13012 [stat.ML]

(or arXiv:2505.13012v3 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2505.13012 Focus to learn more arXiv-issued DOI via DataCite

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