# Deep neural networks algorithms for stochastic control problems on finite horizon: numerical applications

arXiv: https://arxiv.org/abs/1812.05916 · HTML: https://mlsanity.com/paper/1812.05916/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Dec 2018.

## Built on by (most cited first, 16 of 16)

- [SympOCnet: Solving optimal control problems with applications to high-dimensional multi-agent path planning problems](https://mlsanity.com/paper/2201.05475/) (2022)
- [Data-Driven Merton's Strategies via Policy Randomization](https://mlsanity.com/paper/2312.11797/) (2023)
- [Deep Learning for Continuous-Time Stochastic Control with Jumps](https://mlsanity.com/paper/2505.15602/) (2025)
- [Neural network architectures using min-plus algebra for solving certain high dimensional optimal control problems and Hamilton-Jacobi PDEs](https://mlsanity.com/paper/2105.03336/) (2021)
- [Temporal Difference Learning with Continuous Time and State in the Stochastic Setting](https://mlsanity.com/paper/2202.07960/) (2022)
- [Machine learning for option pricing: an empirical investigation of network architectures](https://mlsanity.com/paper/2307.07657/) (2023)
- [Performance of a Markovian neural network versus dynamic programming on a fishing control problem](https://mlsanity.com/paper/2109.06856/) (2021)
- [Langevin algorithms for Markovian Neural Networks and Deep Stochastic control](https://mlsanity.com/paper/2212.12018/) (2022)
- [Automatic model training under restrictive time constraints](https://mlsanity.com/paper/2104.10746/) (2021)
- [Policy Gradient Optimal Correlation Search for Variance Reduction in Monte Carlo simulation and Maximum Optimal Transport](https://mlsanity.com/paper/2307.12703/) (2023)
- [Deep multitask neural networks for solving some stochastic optimal control problems](https://mlsanity.com/paper/2401.12923/) (2024)
- [Adversarial Reinforcement Learning: A Duality-Based Approach To Solving Optimal Control Problems](https://mlsanity.com/paper/2506.00801/) (2025)
- [Finite-Agent Stochastic Differential Games on Large Graphs: II. Graph-Based Architectures](https://mlsanity.com/paper/2509.12484/) (2025)
- [Convergence analysis of controlled particle systems arising in deep learning: from finite to infinite sample size](https://mlsanity.com/paper/2404.05185/) (2024)
- [Mean-Field Generalisation Bounds for Learning Controls in Stochastic Environments](https://mlsanity.com/paper/2508.16001/) (2025)
- [A Posteriori Error Analysis for Decoupled Neural Approximations of Fully Coupled FBSDEs with Control Mismatch](https://mlsanity.com/paper/2606.29474/) (2026)

## Abstract (arXiv)

This paper presents several numerical applications of deep learning-based algorithms that have been introduced in [HPBL18]. Numerical and comparative tests using TensorFlow illustrate the performance of our different algorithms, namely control learning by performance iteration (algorithms NNcontPI and ClassifPI), control learning by hybrid iteration (algorithms Hybrid-Now and Hybrid-LaterQ), on the 100-dimensional nonlinear PDEs examples from [EHJ17] and on quadratic backward stochastic differential equations as in [CR16]. We also performed tests on low-dimension control problems such as an option hedging problem in finance, as well as energy storage problems arising in the valuation of gas storage and in microgrid management. Numerical results and comparisons to quantization-type algorithms Qknn, as an efficient algorithm to numerically solve low-dimensional control problems, are also provided; and some corresponding codes are available on https://github.com/comeh/.