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 large-scale system, in 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 im-portant 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 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 system is new in team literature and its well-posedness is also challenging. We address this is-sue under mild conditions. Related asymptotic optimality is also established.