Thompson Sampling for Learning Parameterized Markov Decision Processes

TL;DR

This paper introduces a Thompson sampling approach for parameterized Markov Decision Processes, providing a regret bound that scales logarithmically with time and depends on the information complexity of the model.

Contribution

It develops a Thompson sampling algorithm for parameterized MDPs with a regret analysis that applies to general priors without requiring conjugacy or specific structure.

Findings

Regret scales logarithmically with time with high probability.

The regret bound depends on the Kullback-Leibler geometry of the parameter space.

The method applies to priors with significant probability near the true model.

Abstract

We consider reinforcement learning in parameterized Markov Decision Processes (MDPs), where the parameterization may induce correlation across transition probabilities or rewards. Consequently, observing a particular state transition might yield useful information about other, unobserved, parts of the MDP. We present a version of Thompson sampling for parameterized reinforcement learning problems, and derive a frequentist regret bound for priors over general parameter spaces. The result shows that the number of instants where suboptimal actions are chosen scales logarithmically with time, with high probability. It holds for prior distributions that put significant probability near the true model, without any additional, specific closed-form structure such as conjugate or product-form priors. The constant factor in the logarithmic scaling encodes the information complexity of learning the MDP in terms of the Kullback-Leibler geometry of the parameter space.