论文标题
扩展的平均场控制问题：混乱结果的传播
Extended mean field control problem: a propagation of chaos result
论文作者
论文摘要
在本文中，我们研究了$扩展$平均场控制问题，这是一类McKean-Vlasov随机控制问题，其中状态动力和奖励功能取决于受控状态的关节（条件）分布和控制过程。通过考虑适当的受控fokker-planck方程，我们可以在衡量值的过程中提出优化问题，并在适当的假设下证明此优化问题与$扩展的$平均型号控制问题之间的等价性。此外，在这个新的优化问题的帮助下，我们建立了相关的极限理论，即$扩展$平均野外控制问题是一个大人群控制问题的极限，在该问题中，通过状态和控制过程的经验分布实现了相互作用。
In this paper, we study the $extended$ mean field control problem, which is a class of McKean-Vlasov stochastic control problem where the state dynamics and the reward functions depend upon the joint (conditional) distribution of the controlled state and the control process. By considering an appropriate controlled Fokker-Planck equation, we can formulate an optimization problem over a space of measure-valued processes and, under suitable assumptions, prove the equivalence between this optimization problem and the $extended$ mean-field control problem. Moreover, with the help of this new optimization problem, we establish the associated limit theory i.e. the $extended$ mean field control problem is the limit of a large population control problem where the interactions are achieved via the empirical distribution of state and control processes.
