We discuss a multiple-play multi-armed bandit (MAB) problem in which several arms are selected at each round. Recently, Thompson sampling (TS), a randomized algorithm with a Bayesian spirit, has attracted much attention for its empirically excellent performance, and it is revealed to have an optimal regret bound in the standard single-play MAB problem. In this paper, we propose the multiple-play Thompson sampling (MP-TS) algorithm, an extension of TS to the multiple-play MAB problem, and discuss its regret analysis. We prove that MP-TS for binary rewards has the optimal regret upper bound that matches the regret lower bound provided by Anantharam et al. (1987). Therefore, MP-TS is the first computationally efficient algorithm with optimal regret. A set of computer simulations was also conducted, which compared MP-TS with state-of-the-art algorithms. We also propose a modification of MP-TS, which is shown to have better empirical performance.
Optimal Regret Analysis of Thompson Sampling in Stochastic Multi-armed Bandit Problem with Multiple Plays
Junpei Komiyama,J. Honda,H. Nakagawa
Published 2015 in International Conference on Machine Learning
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- Publication year
2015
- Venue
International Conference on Machine Learning
- Publication date
2015-06-02
- Fields of study
Mathematics, Computer Science
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