A Near-Optimal Change-Detection Based Algorithm for Piecewise-Stationary Combinatorial Semi-Bandits

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, \texttt{GLR-CUCB}, which incorporates an efficient combinatorial semi-bandit algorithm, \texttt{CUCB}, with an almost parameter-free change-point detector, the \emph{Generalized Likelihood Ratio Test} (GLRT). Our analysis shows that the regret of \texttt{GLR-CUCB} is upper bounded by $\mathcal{O}(\sqrt{NKT\log T})$, 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 $\Omega (\sqrt{NKT}$), 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 $\Omega (\sqrt{T})$. Numerical experiments on both synthetic and real-world datasets demonstrate the superiority of \texttt{GLR-CUCB} compared to other state-of-the-art algorithms.

Accepted by AAAI 2020

References in corpus (12)

• Analysis of Thompson Sampling for the multi-armed bandit problem
• Unbiased Offline Evaluation of Contextual-bandit-based News Article Recommendation Algorithms
• Tight Regret Bounds for Stochastic Combinatorial Semi-Bandits
• Combinatorial Bandits Revisited
• Reliable Crowdsourcing for Multi-Class Labeling using Coding Theory
• Nearly Optimal Adaptive Procedure with Change Detection for Piecewise-Stationary Bandit
• Thompson Sampling for Combinatorial Semi-Bandits
• Thompson Sampling in Switching Environments with Bayesian Online Change Point Detection
• Beating Stochastic and Adversarial Semi-bandits Optimally and Simultaneously
• Mixture Martingales Revisited with Applications to Sequential Tests and Confidence Intervals
• Efficient Change-Point Detection for Tackling Piecewise-Stationary Bandits
• Combinatorial Semi-Bandit in the Non-Stationary Environment