  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.
