Provable Anytime Ensemble Sampling Algorithms in Nonlinear Contextual Bandits

arXiv:2510.10730v2 Announce Type: replace-cross 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 (GLM-ES) for generalized linear bandits and Neural Ensemble Sampling (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 widetilde{O}(d^{3/2} sqrt{T} + d^{4}) for GLM-ES and widetilde{{O}}(widetilde{d}^{3/2} sqrt{T}) for Neural-ES, where d is the dimension of feature vectors, widetilde{d} is the effective dimension of a neural tangent kernel (NTK) matrix and T is the number of rounds. The regret bound of GLM-ES matches the state-of-the-art result of randomized exploration algorithms in generalized linear bandit setting. In the theoretical analysis, we introduce techniques that address challenges specific to nonlinear models. Practically, we remove fixed-time horizon assumption by developing anytime versions of our algorithms, suitable when T is unknown. Finally, we empirically evaluate GLM-ES, 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.

Source: arXiv cs.AI | 2026-05-12