# Deep neural networks algorithms for stochastic control problems on finite horizon: convergence analysis

arXiv: https://arxiv.org/abs/1812.04300 · HTML: https://mlsanity.com/paper/1812.04300/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Dec 2018.

## Built on by (most cited first, 24 of 24)

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- [A Machine Learning Algorithm for Finite-Horizon Stochastic Control Problems in Economics](https://mlsanity.com/paper/2411.08668/) (2024)
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- [Markov Decision Processes of the Third Kind: Learning Distributions by Policy Gradient Descent](https://mlsanity.com/paper/2602.06567/) (2026)
- [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 develops algorithms for high-dimensional stochastic control problems based on deep learning and dynamic programming. Unlike classical approximate dynamic programming approaches, we first approximate the optimal policy by means of neural networks in the spirit of deep reinforcement learning, and then the value function by Monte Carlo regression. This is achieved in the dynamic programming recursion by performance or hybrid iteration, and regress now methods from numerical probabilities. We provide a theoretical justification of these algorithms. Consistency and rate of convergence for the control and value function estimates are analyzed and expressed in terms of the universal approximation error of the neural networks, and of the statistical error when estimating network function, leaving aside the optimization error. Numerical results on various applications are presented in a companion paper (arxiv.org/abs/1812.05916) and illustrate the performance of the proposed algorithms.