# Deep Forward-Backward SDEs for Min-max Control

arXiv: https://arxiv.org/abs/1906.04771 · HTML: https://mlsanity.com/paper/1906.04771/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2019.

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

- [Learning Stochastic Optimal Policies via Gradient Descent](https://mlsanity.com/paper/2106.03780/) (2021)
- [Decentralized Safe Multi-agent Stochastic Optimal Control using Deep FBSDEs and ADMM](https://mlsanity.com/paper/2202.10658/) (2022)
- [Langevin algorithms for Markovian Neural Networks and Deep Stochastic control](https://mlsanity.com/paper/2212.12018/) (2022)
- [Deep Graphic FBSDEs for Opinion Dynamics Stochastic Control](https://mlsanity.com/paper/2204.02506/) (2022)
- [Policy Gradient Optimal Correlation Search for Variance Reduction in Monte Carlo simulation and Maximum Optimal Transport](https://mlsanity.com/paper/2307.12703/) (2023)
- [Deep L1 Stochastic Optimal Control Policies for Planetary Soft-landing](https://mlsanity.com/paper/2109.00183/) (2021)

## Abstract (arXiv)

This paper presents a novel approach to numerically solve stochastic differential games for nonlinear systems. The proposed approach relies on the nonlinear Feynman-Kac theorem that establishes a connection between parabolic deterministic partial differential equations and forward-backward stochastic differential equations. Using this theorem the Hamilton-Jacobi-Isaacs partial differential equation associated with differential games is represented by a system of forward-backward stochastic differential equations. Numerical solution of the aforementioned system of stochastic differential equations is performed using importance sampling and a Long-Short Term Memory recurrent neural network, which is trained in an offline fashion. The resulting algorithm is tested on two example systems in simulation and compared against the standard risk neutral stochastic optimal control formulations.