DeepAI AI Chat
Log In Sign Up

Deep Learning Approximation for Stochastic Control Problems

by   Jiequn Han, et al.

Many real world stochastic control problems suffer from the "curse of dimensionality". To overcome this difficulty, we develop a deep learning approach that directly solves high-dimensional stochastic control problems based on Monte-Carlo sampling. We approximate the time-dependent controls as feedforward neural networks and stack these networks together through model dynamics. The objective function for the control problem plays the role of the loss function for the deep neural network. We test this approach using examples from the areas of optimal trading and energy storage. Our results suggest that the algorithm presented here achieves satisfactory accuracy and at the same time, can handle rather high dimensional problems.


page 1

page 2

page 3

page 4


Deep neural networks algorithms for stochastic control problems on finite horizon, part I: convergence analysis

This paper develops algorithms for high-dimensional stochastic control p...

Quasi-Monte Carlo sampling for machine-learning partial differential equations

Solving partial differential equations in high dimensions by deep neural...

Martingale Functional Control variates via Deep Learning

We propose black-box-type control variate for Monte Carlo simulations by...

Deep neural network approximation for high-dimensional parabolic Hamilton-Jacobi-Bellman equations

The approximation of solutions to second order Hamilton–Jacobi–Bellman (...

Gradient-augmented Supervised Learning of Optimal Feedback Laws Using State-dependent Riccati Equations

A supervised learning approach for the solution of large-scale nonlinear...

Challenges in High-dimensional Reinforcement Learning with Evolution Strategies

Evolution Strategies (ESs) have recently become popular for training dee...

A control method for solving high-dimensional Hamiltonian systems through deep neural networks

In this paper, we mainly focus on solving high-dimensional stochastic Ha...