TY - GEN
T1 - A near-optimal change-detection based algorithm for piecewise-stationary combinatorial semi-bandits
AU - Zhou, Huozhi
AU - Wang, Lingda
AU - Varshney, Lav R.
AU - Lim, Ee Peng
N1 - Publisher Copyright:
Copyright © 2020, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.
PY - 2020
Y1 - 2020
N2 - 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.
AB - 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.
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M3 - Conference contribution
AN - SCOPUS:85106413687
T3 - AAAI 2020 - 34th AAAI Conference on Artificial Intelligence
SP - 6933
EP - 6940
BT - AAAI 2020 - 34th AAAI Conference on Artificial Intelligence
PB - American Association for Artificial Intelligence (AAAI) Press
T2 - 34th AAAI Conference on Artificial Intelligence, AAAI 2020
Y2 - 7 February 2020 through 12 February 2020
ER -