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 algorithms improve the training on various stochastic control problems like hedging and resource management, and for different choices of gradient descent methods.
Code (1)
Tasks
ManagementSimilar Papers 제목 키워드 기반
Continuous-Time Reinforcement Learning for Controlled Hawkes Jump-Diffusions
We study stochastic control of multivariate Hawkes-driven stochastic differential equations with machine learning algorithms in a non-Markovian setting. Due to the path dependence of the memory of the Hawkes intensity, t…
Reinforcement LearningOn couplings for kinetic Langevin diffusions
For the kinetic Langevin diffusion and its splitting discretizations, the hypoelliptic noise structure makes the relationship between couplings and total variation (TV) bounds more subtle than in the elliptic case. We es…
Using Echo State Networks to Approximate Value Functions for Control
An Echo State Network (ESN) is a type of single-layer recurrent neural network with randomly-chosen internal weights and a trainable output layer. We prove under mild conditions that a sufficiently large Echo State Netwo…
Central Limit Theorem for Two-Timescale Stochastic Approximation with Markovian Noise: Theory and Applications
Two-timescale stochastic approximation (TTSA) is among the most general frameworks for iterative stochastic algorithms. This includes well-known stochastic optimization methods such as SGD variants and those designed for…
Stochastic OptimizationDeep Learning for Constrained Utility Maximisation
This paper proposes two algorithms for solving stochastic control problems with deep learning, with a focus on the utility maximisation problem. The first algorithm solves Markovian problems via the Hamilton Jacobi Bellm…
Deep Learning