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Analysis and Design of Thompson Sampling for Stochastic Partial Monitoring
Taira Tsuchiya · Junya Honda · Masashi Sugiyama

Wed Dec 09 09:00 PM -- 11:00 PM (PST) @ Poster Session 4 #1279
We investigate finite stochastic partial monitoring, which is a general model for sequential learning with limited feedback. While Thompson sampling is one of the most promising algorithms on a variety of online decision-making problems, its properties for stochastic partial monitoring have not been theoretically investigated, and the existing algorithm relies on a heuristic approximation of the posterior distribution. To mitigate these problems, we present a novel Thompson-sampling-based algorithm, which enables us to exactly sample the target parameter from the posterior distribution. Besides, we prove that the new algorithm achieves the logarithmic problem-dependent expected pseudo-regret $\mathsf{O}(\log T)$ for a linearized variant of the problem with local observability. This result is the first regret bound of Thompson sampling for partial monitoring, which also becomes the first logarithmic regret bound of Thompson sampling for linear bandits.

Author Information

Taira Tsuchiya (The University of Tokyo / RIKEN)
Junya Honda (Kyoto University / RIKEN)
Masashi Sugiyama (RIKEN / University of Tokyo)

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