SIAM Journal on Control and Optimization, Volume 59, Issue 2, Page 777-804, January 2021.
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 a mild conditional independence condition. 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 assumed either a classical information structure or a static information structure. We also apply these results to the important special case of linear quadratic Gaussian (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.

中文翻译：

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凸对称随机动态团队的最优策略及其均值场极限

SIAM控制与优化杂志，第59卷，第2期，第777-804页，2021年1月。
本文研究了分散信息结构下具有有限和无限时间范围的凸型随机动态团队问题。首先，我们引入两个概念，称为可交换团队和对称信息结构。我们表明，在凸可交换团队问题中，最优策略表现出对称结构。对于温和的条件独立条件下的一类凸动态团队问题，我们给出了这类对称最优团队的特征。此外，通过集中度量参数，我们建立了具有$ N $决策者的团队的最优策略与具有无限多决策者的对称均值场团队的相应最优策略的收敛性。作为副产品，我们提出凸均值场团队的存在结果，与假设是经典信息结构或静态信息结构的文献中的相关结果相比，本文的主要贡献在于系统中的信息结构。我们还将这些结果应用于线性二次高斯（LQG）团队问题的重要特例，其中对于时间有限的部分嵌套LQG团队问题，已知最优策略是线性的，对于无限远景问题，最优线性尚未完全建立政策。我们还研究了具有对称部分嵌套信息结构的平均成本有限和无限期动态团队问题，并获得了建立最优策略线性度的全局最优解。