Near-Optimal Algorithm for Non-Stationary Kernelized Bandits

Shogo Iwazaki, Shion Takeno
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:406-414, 2025.

Abstract

This paper studies a non-stationary kernelized bandit (KB) problem, also called time-varying Bayesian optimization, where one seeks to minimize the regret under an unknown reward function that varies over time. In particular, we focus on a near-optimal algorithm whose regret upper bound matches the regret lower bound. For this goal, we show the first algorithm-independent regret lower bound for non-stationary KB with squared exponential and Matérn kernels, which reveals that an existing optimization-based KB algorithm with slight modification is near-optimal. However, this existing algorithm suffers from feasibility issues due to its huge computational cost. Therefore, we propose a novel near-optimal algorithm called restarting phased elimination with random permutation (R-PERP), which bypasses the huge computational cost. A technical key point is the simple permutation procedures of query candidates, which enable us to derive a novel tighter confidence bound tailored to the non-stationary problems.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-iwazaki25a, title = {Near-Optimal Algorithm for Non-Stationary Kernelized Bandits}, author = {Iwazaki, Shogo and Takeno, Shion}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {406--414}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/iwazaki25a/iwazaki25a.pdf}, url = {https://proceedings.mlr.press/v258/iwazaki25a.html}, abstract = {This paper studies a non-stationary kernelized bandit (KB) problem, also called time-varying Bayesian optimization, where one seeks to minimize the regret under an unknown reward function that varies over time. In particular, we focus on a near-optimal algorithm whose regret upper bound matches the regret lower bound. For this goal, we show the first algorithm-independent regret lower bound for non-stationary KB with squared exponential and Matérn kernels, which reveals that an existing optimization-based KB algorithm with slight modification is near-optimal. However, this existing algorithm suffers from feasibility issues due to its huge computational cost. Therefore, we propose a novel near-optimal algorithm called restarting phased elimination with random permutation (R-PERP), which bypasses the huge computational cost. A technical key point is the simple permutation procedures of query candidates, which enable us to derive a novel tighter confidence bound tailored to the non-stationary problems.} }
Endnote
%0 Conference Paper %T Near-Optimal Algorithm for Non-Stationary Kernelized Bandits %A Shogo Iwazaki %A Shion Takeno %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-iwazaki25a %I PMLR %P 406--414 %U https://proceedings.mlr.press/v258/iwazaki25a.html %V 258 %X This paper studies a non-stationary kernelized bandit (KB) problem, also called time-varying Bayesian optimization, where one seeks to minimize the regret under an unknown reward function that varies over time. In particular, we focus on a near-optimal algorithm whose regret upper bound matches the regret lower bound. For this goal, we show the first algorithm-independent regret lower bound for non-stationary KB with squared exponential and Matérn kernels, which reveals that an existing optimization-based KB algorithm with slight modification is near-optimal. However, this existing algorithm suffers from feasibility issues due to its huge computational cost. Therefore, we propose a novel near-optimal algorithm called restarting phased elimination with random permutation (R-PERP), which bypasses the huge computational cost. A technical key point is the simple permutation procedures of query candidates, which enable us to derive a novel tighter confidence bound tailored to the non-stationary problems.
APA
Iwazaki, S. & Takeno, S.. (2025). Near-Optimal Algorithm for Non-Stationary Kernelized Bandits. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:406-414 Available from https://proceedings.mlr.press/v258/iwazaki25a.html.

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