A topology for Team Policies and Existence of Optimal Team Policies in Stochastic Team Theory
Provides theoretical foundations for optimal policy existence in stochastic team theory, addressing a known gap for dynamic teams.
The paper proves existence of team-optimal policies for static teams and a class of sequential dynamic teams under regularity conditions, applying results to Witsenhausen's counterexample and the Gaussian relay channel.
In this paper, we establish the existence of team-optimal policies for static teams and a class of sequential dynamic teams. We first consider the static team problems and show the existence of optimal policies under certain regularity conditions on the observation channels by introducing a topology on the set of policies. Then we consider sequential dynamic teams and establish the existence of an optimal policy via the static reduction method of Witsenhausen. We apply our findings to the well-known counterexample of Witsenhausen and the Gaussian relay channel problem.