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Poster
Learning Unknown Markov Decision Processes: A Thompson Sampling Approach
Yi Ouyang · Mukul Gagrani · Ashutosh Nayyar · Rahul Jain

Wed Dec 06 06:30 PM -- 10:30 PM (PST) @ Pacific Ballroom #16 #None
We consider the problem of learning an unknown Markov Decision Process (MDP) that is weakly communicating in the infinite horizon setting. We propose a Thompson Sampling-based reinforcement learning algorithm with dynamic episodes (TSDE). At the beginning of each episode, the algorithm generates a sample from the posterior distribution over the unknown model parameters. It then follows the optimal stationary policy for the sampled model for the rest of the episode. The duration of each episode is dynamically determined by two stopping criteria. The first stopping criterion controls the growth rate of episode length. The second stopping criterion happens when the number of visits to any state-action pair is doubled. We establish $\tilde O(HS\sqrt{AT})$ bounds on expected regret under a Bayesian setting, where $S$ and $A$ are the sizes of the state and action spaces, $T$ is time, and $H$ is the bound of the span. This regret bound matches the best available bound for weakly communicating MDPs. Numerical results show it to perform better than existing algorithms for infinite horizon MDPs.

Author Information

Yi Ouyang (University of California, Berkeley)
Mukul Gagrani (University of Southern California)
Ashutosh Nayyar (University of Southern California)
Rahul Jain (University of Southern California)