# Solving stochastic optimal control problem via stochastic maximum principle with deep learning method

arXiv: https://arxiv.org/abs/2007.02227 · HTML: https://mlsanity.com/paper/2007.02227/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jul 2020.

## Built on by (most cited first, 6 of 6)

- [A Policy Gradient Framework for Stochastic Optimal Control Problems with Global Convergence Guarantee](https://mlsanity.com/paper/2302.05816/) (2023)
- [Deep Learning for Continuous-Time Stochastic Control with Jumps](https://mlsanity.com/paper/2505.15602/) (2025)
- [A deep learning method for solving stochastic optimal control problems driven by fully-coupled FBSDEs](https://mlsanity.com/paper/2204.05796/) (2022)
- [Solving a class of stochastic optimal control problems by physics-informed neural networks](https://mlsanity.com/paper/2402.15592/) (2024)
- [A Schr"odinger Eigenfunction Method for Long-Horizon Stochastic Optimal Control](https://mlsanity.com/paper/2603.23173/) (2026)
- [Deep Learning for Reflected BSDEs: Regularization and Error Analysis](https://mlsanity.com/paper/2609.05434/) (2026)

## Abstract (arXiv)

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.