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<p>This paper reviews the mean field social (MFS) optimal control problem for multi-agent dynamic systems and the mean-field-type (MFT) optimal control problem for single-agent dynamic systems within the linear quadratic (LQ) framework. For the MFS control problem, this review discusses the existing conclusions on optimization in dynamic systems affected by both additive and multiplicative noises. In exploring MFT optimization, the authors first revisit researches associated with single-player systems constrained by these dynamics. The authors then extend the proposed review to scenarios that include multiple players engaged in Nash games, Stackelberg games, and cooperative Pareto games. Finally, the paper concludes by emphasizing future research on intelligent algorithms for mean field optimization, particularly using reinforcement learning method to design strategies for models with unknown parameters.</p>

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A Brief Review on Mean Field Optimal Control Problem from a Linear Quadratic Perspective

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • Xiushan Jiang,
  • Daniel W. C. Ho,
  • Weihai Zhang

摘要

This paper reviews the mean field social (MFS) optimal control problem for multi-agent dynamic systems and the mean-field-type (MFT) optimal control problem for single-agent dynamic systems within the linear quadratic (LQ) framework. For the MFS control problem, this review discusses the existing conclusions on optimization in dynamic systems affected by both additive and multiplicative noises. In exploring MFT optimization, the authors first revisit researches associated with single-player systems constrained by these dynamics. The authors then extend the proposed review to scenarios that include multiple players engaged in Nash games, Stackelberg games, and cooperative Pareto games. Finally, the paper concludes by emphasizing future research on intelligent algorithms for mean field optimization, particularly using reinforcement learning method to design strategies for models with unknown parameters.