Provable Anytime Ensemble Sampling Algorithms in Nonlinear Contextual Bandits

• URL: http://arxiv.org/abs/2510.10730v1
• Date: Sun, 12 Oct 2025 18:05:53 GMT
• Title: Provable Anytime Ensemble Sampling Algorithms in Nonlinear Contextual Bandits
• Authors: Jiazheng Sun, Weixin Wang, Pan Xu,
• Abstract summary: Generalized Linear Ensemble Sampling (textttGLM-ES) for generalized linear bandits and Neural Ensemble Sampling (textttNeural-ES) for neural contextual bandits.<n>We prove high-probability frequentist regret bounds of $mathcalO(d3/2 sqrtT + d9/2)$ for textttGLM-ES and $mathcalO(widetilded sqrtT)$ for text
• Score: 10.131895986034314
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We provide a unified algorithmic framework for ensemble sampling in nonlinear contextual bandits and develop corresponding regret bounds for two most common nonlinear contextual bandit settings: Generalized Linear Ensemble Sampling (\texttt{GLM-ES}) for generalized linear bandits and Neural Ensemble Sampling (\texttt{Neural-ES}) for neural contextual bandits. Both methods maintain multiple estimators for the reward model parameters via maximum likelihood estimation on randomly perturbed data. We prove high-probability frequentist regret bounds of $\mathcal{O}(d^{3/2} \sqrt{T} + d^{9/2})$ for \texttt{GLM-ES} and $\mathcal{O}(\widetilde{d} \sqrt{T})$ for \texttt{Neural-ES}, where $d$ is the dimension of feature vectors, $\widetilde{d}$ is the effective dimension of a neural tangent kernel matrix, and $T$ is the number of rounds. These regret bounds match the state-of-the-art results of randomized exploration algorithms in nonlinear contextual bandit settings. In the theoretical analysis, we introduce techniques that address challenges specific to nonlinear models. Practically, we remove fixed-time horizon assumptions by developing anytime versions of our algorithms, suitable when $T$ is unknown. Finally, we empirically evaluate \texttt{GLM-ES}, \texttt{Neural-ES}, and their anytime variants, demonstrating strong performance. Overall, our results establish ensemble sampling as a provable and practical randomized exploration approach for nonlinear contextual bandits.

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