Efficiently Solving MDPs with Stochastic Mirror Descent

• URL: http://arxiv.org/abs/2008.12776v1
• Date: Fri, 28 Aug 2020 17:58:40 GMT
• Title: Efficiently Solving MDPs with Stochastic Mirror Descent
• Authors: Yujia Jin and Aaron Sidford
• Abstract summary: We present a unified framework for approximately solving infinite-horizon Markov decision processes (MDPs) given a linear model. We achieve these results through a more general mirror descent framework for solving bigenerative saddle-point problems with simplex and box domains.
• Score: 38.30919646721354
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $A_{tot}$ total state-action pairs and mixing time bound $t_{mix}$ our method computes an $\epsilon$-optimal policy with an expected $\widetilde{O}(t_{mix}^2 A_{tot} \epsilon^{-2})$ samples from the state-transition matrix, removing the ergodicity dependence of prior art. When applied to a $\gamma$-discounted MDP with $A_{tot}$ total state-action pairs our method computes an $\epsilon$-optimal policy with an expected $\widetilde{O}((1-\gamma)^{-4} A_{tot} \epsilon^{-2})$ samples, matching the previous state-of-the-art up to a $(1-\gamma)^{-1}$ factor. Both methods are model-free, update state values and policies simultaneously, and run in time linear in the number of samples taken. We achieve these results through a more general stochastic mirror descent framework for solving bilinear saddle-point problems with simplex and box domains and we demonstrate the flexibility of this framework by providing further applications to constrained MDPs.

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