Nearly-Optimal Algorithm for Adversarial Kernelized Bandits

• URL: http://arxiv.org/abs/2605.10299v1
• Date: Mon, 11 May 2026 09:56:18 GMT
• Title: Nearly-Optimal Algorithm for Adversarial Kernelized Bandits
• Abstract summary: This paper studies kernelized bandits (also known as Gaussian process bandits) in an adversarial environment.<n>We show that the exponential-weight algorithm achieves $tildeO(sqrtT _T)$ adversarial regret, where $T$ and $_T$ denote the number of total rounds and the maximum information gain.
• Score: 5.753274939310764
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper studies kernelized bandits (also known as Gaussian process bandits) in an adversarial environment, where the reward functions in a known reproducing kernel Hilbert space (RKHS) may be adversarially chosen at each round. We show that the exponential-weight algorithm achieves $\tilde{O}(\sqrt{T γ_T})$ adversarial regret, where $T$ and $γ_T$ denote the number of total rounds and the maximum information gain, respectively. For squared exponential (SE) and $ν$-Matérn kernels, we also show algorithm-independent lower bounds that guarantee the optimality of our algorithm up to polylogarithmic factors. Furthermore, we present a computationally efficient variant of our algorithm using Nyström approximation while maintaining nearly optimal regret guarantees.

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