Langevin Algorithms for Markovian Neural Networks and Deep Stochastic Control

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 and Layer-Langevin algorithms improve the training on various stochastic control problems like hedging and resource management, and for different choices of gradient descent methods.