2019/08/27 by Huozhi Zhou, Zhou, Huozhi, Lingda Wang +5
Computer Science · Decision Sciences · #Advanced Bandit Algorithms Research #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Optimization and Search Problems #Reinforcement Learning in Robotics
paper · pdf · doi:10.48550/arxiv.1908.10402
openalex publication_date 2019/08/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the piecewise-stationary combinatorial semi-bandit problem. Compared to the original combinatorial semi-bandit problem, our setting assumes the reward distributions of base arms may change in a piecewise-stationary manner at unknown time steps. We propose an algorithm, GLR-CUCB, which incorporates an efficient combinatorial semi-bandit algorithm, CUCB, with an almost parameter-free change-point detector, the Generalized Likelihood Ratio Test (GLRT). Our analysis shows that the regret of GLR-CUCB is upper bounded by O(√NKTlogT), where N is the number of piecewise-stationary segments, K is the number of base arms, and T is the number of time steps. As a complement, we also derive a nearly matching regret lower bound on the order of Ω(√(NKT)), for both piecewise-stationary multi-armed bandits and combinatorial semi-bandits, using information-theoretic techniques and judiciously constructed piecewise-stationary bandit instances. Our lower bound is tighter than the best available regret lower bound, which is Ω(√(T)). Numerical experiments on both synthetic and real-world datasets demonstrate the superiority of GLR-CUCB compared to other state-of-the-art algorithms.