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We propose a novel randomized linear programming algorithm for approximatingthe optimal policy of the discounted Markov decision problem. By leveraging thevalue-policy duality and binary-tree data structures, the algorithm adaptivelysamples state-action-state transitions and makes exponentiated primal-dualupdates. We show that it finds an $\epsilon$-optimal policy using nearly-linearrun time in the worst case. When the Markov decision process is ergodic andspecified in some special data formats, the algorithm finds an$\epsilon$-optimal policy using run time linear in the total number ofstate-action pairs, which is sublinear in the input size. These results providea new venue and complexity benchmarks for solving stochastic dynamic programs.

Randomized Linear Programming Solves the Discounted Markov Decision Problem In Nearly-Linear (Sometimes Sublinear) Running Time