# Deep Learning Approximation for Stochastic Control Problems

arXiv: https://arxiv.org/abs/1611.07422 · HTML: https://mlsanity.com/paper/1611.07422/

## Key facts

- Cited by 55 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Nov 2016.

## Built on by (most cited first, 30 of 55)

- [Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Control](https://mlsanity.com/paper/2409.08861/) (2024)
- [Recent Developments in Machine Learning Methods for Stochastic Control and Games](https://mlsanity.com/paper/2303.10257/) (2023)
- [Finite Expression Method for Solving High-Dimensional Partial Differential Equations](https://mlsanity.com/paper/2206.10121/) (2022)
- [Deep Learning for Mean Field Games and Mean Field Control with Applications to Finance](https://mlsanity.com/paper/2107.04568/) (2021)
- [Non-convergence of Adam and other adaptive stochastic gradient descent optimization methods for non-vanishing learning rates](https://mlsanity.com/paper/2407.08100/) (2024)
- [Signatured Deep Fictitious Play for Mean Field Games with Common Noise](https://mlsanity.com/paper/2106.03272/) (2021)
- [Convergence of a robust deep FBSDE method for stochastic control](https://mlsanity.com/paper/2201.06854/) (2022)
- [Entropy annealing for policy mirror descent in continuous time and space](https://mlsanity.com/paper/2405.20250/) (2024)
- [DeepHAM: A Global Solution Method for Heterogeneous Agent Models with Aggregate Shocks](https://mlsanity.com/paper/2112.14377/) (2021)
- [Mean-field neural networks-based algorithms for McKean-Vlasov control problems *](https://mlsanity.com/paper/2212.11518/) (2022)
- [Data-Driven Merton's Strategies via Policy Randomization](https://mlsanity.com/paper/2312.11797/) (2023)
- [Data-Driven Computational Methods for the Domain of Attraction and Zubov's Equation](https://mlsanity.com/paper/2112.14415/) (2021)
- [Linear convergence of a policy gradient method for some finite horizon continuous time control problems](https://mlsanity.com/paper/2203.11758/) (2022)
- [Generative Neural Operators of Log-Complexity Can Simultaneously Solve Infinitely Many Convex Programs](https://mlsanity.com/paper/2508.14995/) (2025)
- [Deep Learning for Continuous-Time Stochastic Control with Jumps](https://mlsanity.com/paper/2505.15602/) (2025)
- [An application of the splitting-up method for the computation of a neural network representation for the solution for the filtering equations](https://mlsanity.com/paper/2201.03283/) (2022)
- [Temporal Difference Learning with Continuous Time and State in the Stochastic Setting](https://mlsanity.com/paper/2202.07960/) (2022)
- [A brief review of the Deep BSDE method for solving high-dimensional partial differential equations](https://mlsanity.com/paper/2505.17032/) (2025)
- [Online Control-Informed Learning](https://mlsanity.com/paper/2410.03924/) (2024)
- [Solving Optimal Execution Problems via In-Context Operator Networks](https://mlsanity.com/paper/2501.15106/) (2025)
- [Discrete Adjoint Schr"odinger Bridge Sampler](https://mlsanity.com/paper/2602.08243/) (2026)
- [Offline Supervised Learning V.S. Online Direct Policy Optimization: A Comparative Study and A Unified Training Paradigm for Neural Network-Based Optimal Feedback Control](https://mlsanity.com/paper/2211.15930/) (2022)
- [An Efficient On-Policy Deep Learning Framework for Stochastic Optimal Control](https://mlsanity.com/paper/2410.05163/) (2024)
- [Neural Actor-Critic Methods for Hamilton-Jacobi-Bellman PDEs: Asymptotic Analysis and Numerical Studies](https://mlsanity.com/paper/2507.06428/) (2025)
- [Recurrent Neural Networks for Stochastic Control Problems with Delay](https://mlsanity.com/paper/2101.01385/) (2021)
- [Performance of a Markovian neural network versus dynamic programming on a fishing control problem](https://mlsanity.com/paper/2109.06856/) (2021)
- [A deep learning method for solving stochastic optimal control problems driven by fully-coupled FBSDEs](https://mlsanity.com/paper/2204.05796/) (2022)
- [On Parametric Optimal Execution and Machine Learning Surrogates](https://mlsanity.com/paper/2204.08581/) (2022)
- [Neural Network Optimal Feedback Control with Guaranteed Local Stability](https://mlsanity.com/paper/2205.00394/) (2022)
- [Langevin algorithms for Markovian Neural Networks and Deep Stochastic control](https://mlsanity.com/paper/2212.12018/) (2022)

## Abstract (arXiv)

Many real world stochastic control problems suffer from the "curse of dimensionality". To overcome this difficulty, we develop a deep learning approach that directly solves high-dimensional stochastic control problems based on Monte-Carlo sampling. We approximate the time-dependent controls as feedforward neural networks and stack these networks together through model dynamics. The objective function for the control problem plays the role of the loss function for the deep neural network. We test this approach using examples from the areas of optimal trading and energy storage. Our results suggest that the algorithm presented here achieves satisfactory accuracy and at the same time, can handle rather high dimensional problems.