# Langevin algorithms for Markovian Neural Networks and Deep Stochastic control

arXiv: https://arxiv.org/abs/2212.12018 · HTML: https://mlsanity.com/paper/2212.12018/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 34 references that are in the map.
- First posted on arXiv 22 Dec 2022.

## Builds on (most cited first, 18 of 18)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Identifying and attacking the saddle point problem in high-dimensional non-convex optimization](https://mlsanity.com/paper/1406.2572/) (2014)
- [Adding Gradient Noise Improves Learning for Very Deep Networks](https://mlsanity.com/paper/1511.06807/) (2015)
- [Preconditioned Stochastic Gradient Langevin Dynamics for Deep Neural Networks](https://mlsanity.com/paper/1512.07666/) (2015)
- [Deep Hedging](https://mlsanity.com/paper/1802.03042/) (2018)
- [Which Neural Net Architectures Give Rise To Exploding and Vanishing Gradients?](https://mlsanity.com/paper/1801.03744/) (2018)
- [Deep Learning Approximation for Stochastic Control Problems](https://mlsanity.com/paper/1611.07422/) (2016)
- [Noisy Activation Functions](https://mlsanity.com/paper/1603.00391/) (2016)
- [Equilibrated adaptive learning rates for non-convex optimization](https://mlsanity.com/paper/1502.04390/) (2015)
- [Convergence Analysis of Machine Learning Algorithms for the Numerical Solution of Mean Field Control and Games: II -- The Finite Horizon Case](https://mlsanity.com/paper/1908.01613/) (2019)
- [Deep neural networks algorithms for stochastic control problems on finite horizon: convergence analysis](https://mlsanity.com/paper/1812.04300/) (2018)
- [Deep neural networks algorithms for stochastic control problems on finite horizon: numerical applications](https://mlsanity.com/paper/1812.05916/) (2018)
- [ProbAct: A Probabilistic Activation Function for Deep Neural Networks](https://mlsanity.com/paper/1905.10761/) (2019)
- [Deep Forward-Backward SDEs for Min-max Control](https://mlsanity.com/paper/1906.04771/) (2019)
- [Adaptively Preconditioned Stochastic Gradient Langevin Dynamics](https://mlsanity.com/paper/1906.04324/) (2019)
- [Performance of a Markovian neural network versus dynamic programming on a fishing control problem](https://mlsanity.com/paper/2109.06856/) (2021)

## Built on by (most cited first, 2 of 2)

- [Anchored Langevin Algorithms](https://mlsanity.com/paper/2509.19455/) (2025)
- [Fokker-Planck to Callan-Symanzik: evolution of weight matrices under training](https://mlsanity.com/paper/2501.09659/) (2025)

## Abstract (arXiv)

Stochastic Gradient Descent Langevin Dynamics (SGLD) algorithms, which add noise to the classic gradient descent, are known to improve the training of neural networks in some cases where the neural network is very deep. In this paper we study the possibilities of training acceleration for the numerical resolution of stochastic control problems through gradient descent, where the control is parametrized by a neural network. If the control is applied at many discretization times then solving the stochastic control problem reduces to minimizing the loss of a very deep neural network. We numerically show that Langevin algorithms improve the training on various stochastic control problems like hedging and resource management, and for different choices of gradient descent methods.