Recurrent Neural Networks for Stochastic Control Problems with Delay

TL;DR

This paper introduces neural network algorithms, especially recurrent neural networks, to effectively solve complex stochastic control problems with delay, demonstrating superior performance and stability over traditional methods.

Contribution

The paper develops and systematically studies RNN-based algorithms for stochastic control with delay, highlighting their ability to handle path-dependency and infinite delay more effectively.

Findings

RNN architectures outperform feedforward networks in delay problems.

The methods achieve stable and efficient training.

Superior results in portfolio optimization with infinite delay.

Abstract

Stochastic control problems with delay are challenging due to the path-dependent feature of the system and thus its intrinsic high dimensions. In this paper, we propose and systematically study deep neural networks-based algorithms to solve stochastic control problems with delay features. Specifically, we employ neural networks for sequence modeling (\emph{e.g.}, recurrent neural networks such as long short-term memory) to parameterize the policy and optimize the objective function. The proposed algorithms are tested on three benchmark examples: a linear-quadratic problem, optimal consumption with fixed finite delay, and portfolio optimization with complete memory. Particularly, we notice that the architecture of recurrent neural networks naturally captures the path-dependent feature with much flexibility and yields better performance with more efficient and stable training of the network compared to feedforward networks. The superiority is even evident in the case of portfolio optimization with complete memory, which features infinite delay.