A near-optimal change-detection based algorithm for piecewise-stationary combinatorial semi-bandits

Huozhi Zhou, Lingda Wang, Lav R. Varshney, Ee Peng Lim

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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(√NKT log T), 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.

Original languageEnglish (US)
Title of host publicationAAAI 2020 - 34th AAAI Conference on Artificial Intelligence
PublisherAmerican Association for Artificial Intelligence (AAAI) Press
Pages6933-6940
Number of pages8
ISBN (Electronic)9781577358350
StatePublished - 2020
Event34th AAAI Conference on Artificial Intelligence, AAAI 2020 - New York, United States
Duration: Feb 7 2020Feb 12 2020

Publication series

NameAAAI 2020 - 34th AAAI Conference on Artificial Intelligence

Conference

Conference34th AAAI Conference on Artificial Intelligence, AAAI 2020
Country/TerritoryUnited States
CityNew York
Period2/7/202/12/20

ASJC Scopus subject areas

  • Artificial Intelligence

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