Langevin algorithms for Markovian Neural Networks and Deep Stochastic control

Pierre Bras, Gilles Pagès
December 2022
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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.

Type
Conference paper
Publication
In International Joint Conference on Neural Networks IJCNN23
Langevin algorithm SGLD Markovian neural network Stochastic Control Deep neural network Stochastic Optimization
Pierre Bras
Pierre Bras
PhD Student in Applied Mathematics

I am a PhD student under the direction of Gilles Pagès, interested in Machine Learning, Stochastic Optimization and Numerical Probability.

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