A topology for Team Policies and Existence of Optimal Team Policies in Stochastic Team Theory

TL;DR

This paper introduces a new topological framework for analyzing team policies in stochastic team theory, proving the existence of optimal policies for static and certain dynamic teams, with applications to classical problems.

Contribution

It establishes a novel topology on policy sets and proves the existence of optimal team policies for static and some dynamic teams, extending prior results.

Findings

Existence of optimal policies for static teams under regularity conditions

Existence of optimal policies for certain sequential dynamic teams

Application to Witsenhausen's counterexample and Gaussian relay channel

Abstract

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.