Non-signaling Approximations of Stochastic Team Problems

In this paper, we consider non-signaling approximation of finite stochastic teams. We first introduce a hierarchy of team decision rules that can be classified in an increasing order as randomized policies, quantum-correlated policies, and non-signaling policies. Then, we establish an approximation of team-optimal policies for sequential teams via extendible non-signaling policies. We prove that the distance between extendible non-signaling policies and decentralized policies is small if the extension is sufficiently large. Using this result, we establish a linear programming (LP) approximation of sequential teams. Finally, we state an open problem regarding computation of optimal value of quantum-correlated policies.
Comment: There is an error in the proof of Theorem 1. In particular, inequality (d) and equalities (b) and (c) at the end of the proof of Theorem 1 are incorrect. As a result, the main result of the paper is incorrect