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arXiv · 2410.16052

Near-Optimal Algorithm for Non-Stationary Kernelized Bandits

Shogo Iwazaki·Shion Takeno
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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 Mat\'ern 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.

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Shogo Iwazaki, Shion Takeno. 2024-10-21. Near-Optimal Algorithm for Non-Stationary Kernelized Bandits. https://arxiv.org/abs/2410.16052

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