A unified approach to linear-quadratic-Gaussian mean-field team: Homogeneity, heterogeneity and quasi-exchangeability

Abstract

This paper aims to systematically solve stochastic team optimization of a large-scale system, in a linear-quadratic-Gaussian framework. Concretely, the underlying large-scale system involves considerable weakly coupled cooperative agents for which the individual admissible controls: (i) enter the diffusion terms, (ii) are constrained in some closed-convex subsets and (iii) subject to a general partial decentralized information structure. A more important but serious feature: (iv) all agents are heterogenous with continuum instead of finite diversity. Combination of (i)–(iv) yields a quite general modeling of stochastic team-optimization, but on the other hand, also fails current existing techniques of team analysis. In particular, classical team consistency with continuum heterogeneity collapses because of (i). As the resolution, a novel unified approach is proposed under which the intractable continuum heterogeneity can be converted to a more tractable homogeneity. As a trade-off, the underlying randomness is augmented, and all agents become (quasi) weakly exchangeable. Such an approach essentially involves a subtle balance between homogeneity v.s. heterogeneity, and left (prior-sampling)- v.s. right (posterior-sampling) information filtration. Subsequently, the consistency condition (CC) system takes a new type of forward-backward stochastic system with double-projections (due to (ii), (iii)), along with spatial mean on continuum heterogenous index (due to (iv)). Such a system is new in team literature and its well-posedness is also challenging. We address this issue under mild conditions. Related asymptotic optimality is also established.