Convex Symmetric Stochastic Dynamic Teams and Their Mean-Field Limit

Abstract

This paper studies convex stochastic dynamic team problems with finite and infinite time horizons under decentralized information structures. First, we introduce two notions called exchangeable teams and symmetric information structures. We show that in convex exchangeable team problems an optimal policy exhibits a symmetry structure. We give a characterization for such symmetrically optimal teams for a general class of convex dynamic team problems under mild conditional independence conditions. In addition, through concentration of measure arguments, we establish the convergence of optimal policies for teams with N decision makers to the corresponding optimal policies for symmetric mean-field teams with infinitely many decision makers. As a by-product, we present an existence result for convex mean-field teams, where the main contribution of our paper is with respect to the information structure in the system when compared with the related results in the literature that have either assumed a classical information structure or a static information structure. We also apply these results to the important special case of LQG team problems, where while for partially nested LQG team problems with finite time horizons it is known that the optimal policies are linear, for infinite horizon problems the linearity of optimal policies has not been established in full generality. We also study average cost finite and infinite horizon dynamic team problems with a symmetric partially nested information structure and obtain globally optimal solutions where we establish linearity of optimal policies. Moreover, we also study average cost infinite horizon LQG dynamic teams under sparsity and delay constraints.

Zero-Sum Games between Mean-Field Teams: Reachability-Based Analysis under Mean-Field Sharing

“…This example serves to illustrate the reachability-based optimization in equation ( 11) and to demonstrate that the coordinator game value may not exist, contrary to the continuous setting as discussed in (Sanjari, Saldi, and Yüksel 2023).…”

Decentralized Strategies for Finite Population Linear-Quadratic-Gaussian Games and Teams

“…Authors in [1] considered team-optimal control with finite population and partial information. For further literature, see [23] for socially optimal control for major-minor systems, [45] for the team problem with a Markov jump parameter as common random source, [37] for dynamic collective choice by finding a social optimum, [38] for stochastic dynamic teams and their mean-field limit.…”

Social Optima in Mean Field Linear-Quadratic-Gaussian Control with Volatility Uncertainty

“…The study of [32] designed socially optimal strategies by analyzing forwardbackward stochastic differential equations (FBSDEs). For further literature, see [2] for team-optimal control with finite population and partial information, [44] for dynamic collective choice by finding a social optimum, [45,46] for stochastic dynamic teams and their mean field limit, [41] for social optima in economic models subject to idiosyncratic shocks, and [47] for reinforcement learning algorithms for mean field teams.…”

“…Now, we outline our analysis components to be applied, along with the necessary literature comparison to other works. Recently, there have arisen various works (see, e.g., [3,45,46]) for mean field teams discussing the decentralized control and related asymptotic team optimality in the context of LP exchangeable agents. No uncertainty is formulated in their modelings and thus their analysis can be conducted in a positive definite setting.…”