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Title: | Social optima of backward linear-quadratic-Gaussian mean-field teams | Authors: | Feng, X Huang, J Wang, S |
Issue Date: | Dec-2021 | Source: | Applied mathematics and optimization, Dec. 2021, v. 84, no. Suppl 1, p. 651-694 | Abstract: | This paper studies a class of stochastic linear-quadratic-Gaussian (LQG) dynamic optimization problems involving a large number of weakly-coupled heterogeneous agents. By “heterogeneous,” we mean agents are endowed with different types of parameters thus they are not statistically identical. Specifically, discrete-type heterogeneous agents are considered here which are more practical than homogeneous-type agents, and at the same time, more tractable than continuum-type heterogeneous agents. Unlike well-studied mean-field-game, these agents formalize a team with cooperation to minimize some social cost functional. Moreover, unlike standard social optima literature, the state here evolves by some backward stochastic differential equation (BSDE) in which the terminal instead initial condition is specified. Accordingly, the related social cost is represented by some recursive functional for which the initial state is considered. Applying a backward version of person-by-person optimality, we construct an auxiliary control problem for each agent based on decentralized information. The decentralized social strategy is derived by a class of new consistency condition (CC) systems, which are mean-field-type forward-backward stochastic differential equations (FBSDEs). The well-posedness of such consistency condition system is obtained via Riccati decoupling method. The related asymptotic social optimality is also verified. | Keywords: | Asymptotic social optima Backward person-by-person optimality Discrete-type heterogeneous system Initially mixed-coupled FBSDE LQG recursive control Mean-field team |
Publisher: | Springer | Journal: | Applied mathematics and optimization | ISSN: | 0095-4616 | EISSN: | 1432-0606 | DOI: | 10.1007/s00245-021-09782-8 | Rights: | © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021 This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use(https://www.springernature.com/gp/open-research/policies/accepted-manuscript-terms), but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s00245-021-09782-8. |
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