论文标题
McKean-Vlasov动力学最佳控制的代数收敛速率
An algebraic convergence rate for the optimal control of McKean-Vlasov dynamics
论文作者
论文摘要
我们在大量玩家的限制中建立了代数的收敛速率，这是N颗粒随机控制问题的价值函数，涉及相应的McKean-Vlasov问题的价值函数，也称为平均场控制。在存在特质和常见噪声的情况下以及McKean-Vlasov问题的值函数不必平滑的情况下，该速率是在存在特质和常见噪声的情况下获得的。我们的方法依赖于N Lipschitz中的均匀，以及N粒子值函数以及一定浓度不平等的半含量估计。
We establish an algebraic rate of convergence in the large number of players limit of the value functions of N-particle stochastic control problems towards the value function of the corresponding McKean-Vlasov problem also known as mean field control. The rate is obtained in the presence of both idiosyncratic and common noises and in a setting where the value function for the McKean-Vlasov problem need not be smooth. Our approach relies crucially on uniform in N Lipschitz and semi-concavity estimates for the N-particle value functions as well as a certain concentration inequality.
