Efficiently Solving MDPs with Stochastic Mirror Descent

Jul 12, 2020



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 total actions and mixing time bound our method computes an -optimal policy with an expected (^2 ^-2) samples from the state-transition matrix, removing the ergodicity dependence of prior art. When applied to a γ-discounted MDP with A total actions our method computes an eps-optimal policy with an expected ((1-γ)^-4 ^-2) samples, improving over the best-known primal-dual methods while matching the state-of-the-art up to a (1-γ)^-1 factor. Both methods are model-free, update state values and policy simultaneously, and run in time linear in the number of samples taken.



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