Analysis and Design of Thompson Sampling for Stochastic Partial Monitoring

Abstract

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 $\mathrm{O}(\log T)$ 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.

Published version in NeurIPS 2020 (https://proceedings.neurips.cc/paper/2020/hash/649d45bf179296e31731adfd4df25588-Abstract.html), 39 pages, 4 figures

References in corpus (5)

• Further Optimal Regret Bounds for Thompson Sampling
• An Information-Theoretic Approach to Minimax Regret in Partial Monitoring
• An Adaptive Algorithm for Finite Stochastic Partial Monitoring
• Connections Between Mirror Descent, Thompson Sampling and the Information Ratio
• Information Directed Sampling for Linear Partial Monitoring

Cited by in corpus (2)

• Best-of-Both-Worlds Algorithms for Partial Monitoring
• Apple Tasting Revisited: Bayesian Approaches to Partially Monitored Online Binary Classification