Decentralized stochastic decision problems and polynomial optimization

In this paper we consider the problem of computing decentralized control policies in a discrete stochastic decision problem. For the problem we consider, computation of optimal decentralized policies is NP-hard. We present a relaxation method for this problem which computes suboptimal decentralized policies as well as bounds on the optimal achievable value. We then show that policies computed from this relaxation are guaranteed to be within a fixed bound of optimal. The relaxation is derived from an equivalent formulation of this decentralized decision problem as a polynomial optimization problem. The method is illustrated by an example of decentralized detection.