2020/12/11 by Yusha Liu, Yining Wang, Liu, Yusha +3 · 3 citations
Computer Science · Decision Sciences · #Advanced Bandit Algorithms Research #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms #Reinforcement Learning in Robotics
paper · pdf · doi:10.48550/arxiv.2012.06076
openalex publication_date 2020/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider bandit optimization of a smooth reward function, where the goal is cumulative regret minimization. This problem has been studied for α-Hölder continuous (including Lipschitz) functions with 01 to bridge the gap between Lipschitz bandits and infinitely-differentiable models such as linear bandits. For Hölder continuous functions, approaches based on random sampling in bins of a discretized domain suffices as optimal. In contrast, we propose a class of two-layer algorithms that deploy misspecified linear/polynomial bandit algorithms in bins. We demonstrate that the proposed algorithm can exploit higher-order smoothness of the function by deriving a regret upper bound of O(T^(d+α)/(d+2α)) for when α>1, which matches existing lower bound. We also study adaptation to unknown function smoothness over a continuous scale of Hölder spaces indexed by α, with a bandit model selection approach applied with our proposed two-layer algorithms. We show that it achieves regret rate that matches the existing lower bound for adaptation within the α≤ 1 subset.