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We discuss a multiple-play multi-armed bandit (MAB) problem in which severalarms are selected at each round. Recently, Thompson sampling (TS), a randomizedalgorithm with a Bayesian spirit, has attracted much attention for itsempirically excellent performance, and it is revealed to have an optimal regretbound in the standard single-play MAB problem. In this paper, we propose themultiple-play Thompson sampling (MP-TS) algorithm, an extension of TS to themultiple-play MAB problem, and discuss its regret analysis. We prove that MP-TSfor binary rewards has the optimal regret upper bound that matches the regretlower bound provided by Anantharam et al. (1987). Therefore, MP-TS is the firstcomputationally efficient algorithm with optimal regret. A set of computersimulations was also conducted, which compared MP-TS with state-of-the-artalgorithms. We also propose a modification of MP-TS, which is shown to havebetter empirical performance.

Optimal Regret Analysis of Thompson Sampling in Stochastic Multi-armed Bandit Problem with Multiple Plays