We consider the problem of controlling a Markov decision process (MDP) with a large state space, so as to minimize average cost. Since it is in-tractable to compete with the optimal policy for large scale problems, we pursue the more modest goal of competing with a low-dimensional fam-ily of policies. We use the dual linear program-ming formulation of the MDP average cost prob-lem, in which the variable is a stationary distri-bution over state-action pairs, and we consider a neighborhood of a low-dimensional subset of the set of stationary distributions (defined in terms of state-action features) as the comparison class. We propose a technique based on stochastic con-vex optimization and give bounds that show that the performance of our algorithm approaches the best achievable by any policy in the comparison class. Most importantly, this result depends on the size of the comparison class, but not on the size of the state space. Preliminary experiments show the effectiveness of the proposed algorithm in a queuing application. 1.

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