Near-Optimal Regret in Adversarial Kernel Bandits

• URL: http://arxiv.org/abs/2605.26585v1
• Date: Tue, 26 May 2026 06:10:24 GMT
• Title: Near-Optimal Regret in Adversarial Kernel Bandits
• Abstract summary: We study the adversarial kernel bandit problem, in which the loss at each round is induced by an arbitrary bounded element.<n>Our main result bounds the regret by $widetildeObig(sqrtT, d_*(),log|X|big)$, where $d_*()$ is a widely-adopted notion of effective dimension.
• Score: 50.68324062892194
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the adversarial kernel bandit problem, in which the loss at each round is induced by an arbitrary bounded element of a reproducing kernel Hilbert space (RKHS). We propose an exponential-weights algorithm built on a regularized importance-weighted loss estimator, together with an explicit correction term that cancels the bias introduced by the regularization. Our main result bounds the regret by $\widetilde{O}\big(\sqrt{T\, d_*(λ)\,\log|{X}|}\big)$, where $d_*(λ)$ is a widely-adopted notion of effective dimension that captures the complexity of the kernel. Up to logarithmic factors, this matches the known rate achieved in the related stochastic kernel bandit problem. A notable application is the Matérn$(ν,d)$ kernel with smoothness parameter $ν$ on $\mathbb{R}^d$, for which our bound specializes to $\widetilde{O}\big(T^{(ν+d)/(2ν+d)}\big)$, improving over the best-known prior rate of Chatterji et al. [2019] while simultaneously removing the rank-one adversary assumption required by their analysis. Moreover, this rate is the same as the known optimal rate for stochastic kernel bandits, and also matches a lower bound from concurrent work up to a $\log T$ factor.

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