论文标题
扩展平均场控件的最佳规律性及其分段常数近似
Optimal regularity of extended mean field controls and their piecewise constant approximation
论文作者
论文摘要
我们考虑了McKean-Vlasov动力学的控制，其系数在状态和控制中具有平均场相互作用。我们表明，对于一类线性符号平均场控制问题，独特的最佳开环控制允许时间最佳的1/2-Hölder规律性。因此，我们证明可以通过具有分段常数控件和离散时间状态进程的一个值近似的值函数，而欧拉 - 玛丽亚山时间逐步阶段，最多达到1/2级误差，并且可以将最佳控件近似为1/4误差订单。这些结果即使在没有平均场相互作用的情况下也是新颖的。
We consider the control of McKean-Vlasov dynamics whose coefficients have mean field interactions in the state and control. We show that for a class of linear-convex mean field control problems, the unique optimal open-loop control admits the optimal 1/2-Hölder regularity in time. Consequently, we prove that the value function can be approximated by one with piecewise constant controls and discrete-time state processes arising from Euler-Maruyama time stepping, up to an order 1/2 error, and the optimal control can be approximated up to an order 1/4 error. These results are novel even for the case without mean field interaction.
