Deep Learning Approximation for Stochastic Control Problems

TL;DR

This paper introduces a deep learning method that uses neural networks to solve high-dimensional stochastic control problems efficiently, overcoming the curse of dimensionality with promising results in trading and energy storage applications.

Contribution

The paper presents a novel deep learning framework that approximates controls with neural networks and integrates model dynamics, enabling high-dimensional stochastic control solutions.

Findings

Achieves satisfactory accuracy in high-dimensional problems

Handles high-dimensional stochastic control problems effectively

Demonstrates applicability in trading and energy storage

Abstract

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.