论文标题
通过深度学习方法，通过随机最大原理解决随机最佳控制问题
Solving stochastic optimal control problem via stochastic maximum principle with deep learning method
论文作者
论文摘要
在本文中，我们旨在通过深度学习的随机最大原理的视图来解决高维的最佳控制问题。通过引入扩展的汉密尔顿系统，该系统本质上是具有最大条件的FBSDE，我们将原始控制问题重新制定为新问题。提出了三种算法来解决新的控制问题。不同示例的数值结果证明了我们提出的算法的有效性，尤其是在高维情况下。该方法的一个重要应用是计算子线性期望，该期望与一种完全非线性PDE相对应。
In this paper, we aim to solve the high dimensional stochastic optimal control problem from the view of the stochastic maximum principle via deep learning. By introducing the extended Hamiltonian system which is essentially an FBSDE with a maximum condition, we reformulate the original control problem as a new one. Three algorithms are proposed to solve the new control problem. Numerical results for different examples demonstrate the effectiveness of our proposed algorithms, especially in high dimensional cases. And an important application of this method is to calculate the sub-linear expectations, which correspond to a kind of fully nonlinear PDEs.
