# Learning Deep Stochastic Optimal Control Policies using Forward-Backward SDEs

arXiv: https://arxiv.org/abs/1902.03986 · HTML: https://mlsanity.com/paper/1902.03986/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2019.

## Built on by (most cited first, 13 of 13)

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- [Decentralized Safe Multi-agent Stochastic Optimal Control using Deep FBSDEs and ADMM](https://mlsanity.com/paper/2202.10658/) (2022)
- [Deep Graphic FBSDEs for Opinion Dynamics Stochastic Control](https://mlsanity.com/paper/2204.02506/) (2022)
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- [Deep L1 Stochastic Optimal Control Policies for Planetary Soft-landing](https://mlsanity.com/paper/2109.00183/) (2021)
- [Deep Generalized Schr"odinger Bridges: From Image Generation to Solving Mean-Field Games](https://mlsanity.com/paper/2412.20279/) (2024)

## Abstract (arXiv)

In this paper we propose a new methodology for decision-making under uncertainty using recent advancements in the areas of nonlinear stochastic optimal control theory, applied mathematics, and machine learning. Grounded on the fundamental relation between certain nonlinear partial differential equations and forward-backward stochastic differential equations, we develop a control framework that is scalable and applicable to general classes of stochastic systems and decision-making problem formulations in robotics and autonomy. The proposed deep neural network architectures for stochastic control consist of recurrent and fully connected layers. The performance and scalability of the aforementioned algorithm are investigated in three non-linear systems in simulation with and without control constraints. We conclude with a discussion on future directions and their implications to robotics.