On the Existence of Optimal Policies for a Class of Static and Sequential Dynamic Teams

TL;DR

This paper establishes sufficient conditions for the existence of optimal policies in static and certain sequential dynamic teams, broadening the understanding of when optimal solutions can be guaranteed in complex stochastic control problems.

Contribution

It provides new sufficient conditions for the existence of team-optimal solutions in static and dynamic teams, including classes of LQG problems and Witsenhausen's counterexample.

Findings

Optimal solutions exist for static teams with conditionally independent observations.

Extends existence results to a broad class of dynamic LQG team problems.

Includes Witsenhausen's counterexample and Gaussian relay channel as special cases.

Abstract

In this paper, we identify sufficient conditions under which static teams and a class of sequential dynamic teams admit team-optimal solutions. We first investigate the existence of optimal solutions in static teams where the observations of the decision makers are conditionally independent or satisfy certain regularity conditions. Building on these findings and the static reduction method of Witsenhausen, we then extend the analysis to sequential dynamic teams. In particular, we show that a large class of dynamic LQG team problems, including the vector version of the well-known Witsenhausen's counterexample and the Gaussian relay channel problem viewed as a dynamic team, admit team-optimal solutions. Results in this paper substantially broaden the class of stochastic control and team problems with non-classical information known to have optimal solutions.