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We consider finite model approximations of discrete-time partially observedMarkov decision processes (POMDPs) under the discounted cost criterion. Afterconverting the original partially observed stochastic control problem to afully observed one on the belief space, the finite models are obtained throughthe uniform quantization of the state and action spaces of the belief spaceMarkov decision process (MDP). Under mild assumptions on the components of theoriginal model, it is established that the policies obtained from these finitemodels are nearly optimal for the belief space MDP, and so, for the originalpartially observed problem. The assumptions essentially require that the beliefspace MDP satisfies a mild weak continuity condition. We provide examples andintroduce explicit approximation procedures for the quantization of the set ofprobability measures on the state space of POMDP (i.e., belief space).

Finite Model Approximations for Partially Observed Markov Decision Processes with Discounted Cost