Solving stochastic optimal control problem via stochastic maximum principle with deep learning method
This work addresses computational challenges in stochastic optimal control for applications like finance and engineering, offering an incremental improvement by integrating deep learning with existing principles.
The paper tackles high-dimensional stochastic optimal control problems by reformulating them via the stochastic maximum principle and deep learning, proposing three algorithms that demonstrate effectiveness in numerical examples, especially for high-dimensional cases.
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.