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In this paper we propose an algorithm for polynomial-time reinforcementlearning in factored Markov decision processes (FMDPs). The factored optimisticinitial model (FOIM) algorithm, maintains an empirical model of the FMDP in aconventional way, and always follows a greedy policy with respect to its model.The only trick of the algorithm is that the model is initializedoptimistically. We prove that with suitable initialization (i) FOIM convergesto the fixed point of approximate value iteration (AVI); (ii) the number ofsteps when the agent makes non-near-optimal decisions (with respect to thesolution of AVI) is polynomial in all relevant quantities; (iii) the per-stepcosts of the algorithm are also polynomial. To our best knowledge, FOIM is thefirst algorithm with these properties. This extended version contains therigorous proofs of the main theorem. A version of this paper appeared inICML'09.

Optimistic Initialization and Greediness Lead to Polynomial Time Learning in Factored MDPs - Extended Version