Finite Model Approximations and Asymptotic Optimality of Quantized Policies in Decentralized Stochastic Control

Abstract

In this paper, we consider finite model approximations of a large class of static and dynamic team problems where these models are constructed through uniform quantization of the observation and action spaces of the agents. The strategies obtained from these finite models are shown to approximate the optimal cost with arbitrary precision under mild technical assumptions. In particular, quantized team policies are asymptotically optimal. This result is then applied to the Gaussian relay channel problem. This result also applies to Witsenhausen's counterexample, which we had studied individually earlier.

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