Publication Type

Conference Proceeding Article

Version

publishedVersion

Publication Date

12-2020

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 logT), 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 piecewisestationary 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.

Discipline

Databases and Information Systems | Theory and Algorithms

Research Areas

Data Science and Engineering

Publication

Thirty-Third AAAI Conference on Artificial Intelligence: AAAI-20: New York, February 7-12: Proceedings

First Page

1

Last Page

9

ISBN

9781577358350

Identifier

10.1609/aaai.v34i04.6176

Publisher

AAAI Press

City or Country

Menlo Park, CA

Additional URL

https://doi.org/10.1609/aaai.v34i04.6176

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