论文标题
价值函数的规律性和平均场控制问题混乱的定量传播
Regularity of the value function and quantitative propagation of chaos for mean field control problems
论文作者
论文摘要
我们研究了具有强迫和终端数据的大粒子系统的最佳控制限制获得的平均最佳控制问题，该问题被认为不是凸。我们证明，该值函数（已知是Lipschitz连续的，而不是C级1，通常没有凸度，实际上在时间和概率度量的空间和概率措施的开放且密集的子集中实际上是平滑的。结果，我们证明了从这个开放且密集的集合开始的粒子系统最佳解决方案的混乱型结果的新定量传播。
We investigate a mean field optimal control problem obtained in the limit of the optimal control of large particle systems with forcing and terminal data which are not assumed to be convex. We prove that the value function, which is known to be Lipschitz continuous but not of class C 1 , in general, without convexity, is actually smooth in an open and dense subset of the space of times and probability measures. As a consequence, we prove a new quantitative propagation of chaos-type result for the optimal solutions of the particle system starting from this open and dense set.
