Efficiently Solving MDPs with Stochastic Mirror Descent

Part of Proceedings of the International Conference on Machine Learning 1 pre-proceedings (ICML 2020)

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Yujia Jin, Aaron Sidford


<p>In this paper we present a unified framework based on primal-dual stochastic mirror descent for approximately solving infinite-horizon Markov decision processes (MDPs) given a generative model. When applied to an average-reward MDP with \A total actions and mixing time bound \tmix our method computes an \eps-optimal policy with an expected \Otil(\tmix^2 \A \eps^{-2}) samples from the state-transition matrix, removing the ergodicity dependence of prior art. When applied to a \gamma-discounted MDP with A total actions our method computes an eps-optimal policy with an expected \Otil((1-\gamma)^{-4} \A \eps^{-2}) samples, improving over the best-known primal-dual methods while matching the state-of-the-art up to a (1-\gamma)^{-1} factor. Both methods are model-free, update state values and policy simultaneously, and run in time linear in the number of samples taken.</p>