# Variational methods for Reinforcement Learning

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Thomas Furmston,
David Barber
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Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, PMLR 9:241-248, 2010.

#### Abstract

We consider reinforcement learning as solving a Markov decision process with unknown transition distribution. Based on interaction with the environment, an estimate of the transition matrix is obtained from which the optimal decision policy is formed. The classical maximum likelihood point estimate of the transition model does not reflect the uncertainty in the estimate of the transition model and the resulting policies may consequently lack a sufficient degree of exploration. We consider a Bayesian alternative that maintains a distribution over the transition so that the resulting policy takes into account the limited experience of the environment. The resulting algorithm is formally intractable and we discuss two approximate solution methods, Variational Bayes and Expectation Propagation.

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