Efficient kernelized bandit algorithms via exploration distributions

• URL: http://arxiv.org/abs/2506.10091v1
• Date: Wed, 11 Jun 2025 18:23:43 GMT
• Title: Efficient kernelized bandit algorithms via exploration distributions
• Authors: Bingshan Hu, Zheng He, Danica J. Sutherland,
• Abstract summary: We propose a class of computationally efficient kernelized bandit algorithms, which we call GP-Generic.<n>We show that our proposed generic algorithm realizes a wide range of concrete algorithms that achieve $tildeO(gamma_TsqrtT)$ regret bounds.
• Score: 13.86858382375188
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider a kernelized bandit problem with a compact arm set ${X} \subset \mathbb{R}^d $ and a fixed but unknown reward function $f^*$ with a finite norm in some Reproducing Kernel Hilbert Space (RKHS). We propose a class of computationally efficient kernelized bandit algorithms, which we call GP-Generic, based on a novel concept: exploration distributions. This class of algorithms includes Upper Confidence Bound-based approaches as a special case, but also allows for a variety of randomized algorithms. With careful choice of exploration distribution, our proposed generic algorithm realizes a wide range of concrete algorithms that achieve $\tilde{O}(\gamma_T\sqrt{T})$ regret bounds, where $\gamma_T$ characterizes the RKHS complexity. This matches known results for UCB- and Thompson Sampling-based algorithms; we also show that in practice, randomization can yield better practical results.

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