Langevin algorithms for Markovian Neural Networks and Deep Stochastic control

TL;DR

This paper explores how Langevin algorithms can accelerate the training of neural networks used in stochastic control problems, demonstrating improved performance in applications like hedging and resource management.

Contribution

It introduces the application of Langevin algorithms to neural network training for stochastic control, showing their effectiveness in reducing training time and improving solutions.

Findings

Langevin algorithms enhance training efficiency in stochastic control neural networks.

They improve convergence in problems like hedging and resource management.

Langevin methods outperform traditional gradient descent in tested scenarios.

Abstract

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.