Sufficient Markov Decision Processes with Alternating Deep Neural Networks

TL;DR

This paper introduces a method to create low-dimensional Markov decision process representations using deep neural networks, enabling effective decision strategies in complex, real-time mobile health data scenarios.

Contribution

It proposes a novel deep learning-based approach to construct low-dimensional MDP representations that preserve optimal decision-making properties.

Findings

Successfully applied to mobile health data on drinking and smoking

Achieved low-dimensional models that maintain decision optimality

Demonstrated practical utility in real-time intervention settings

Abstract

Advances in mobile computing technologies have made it possible to monitor and apply data-driven interventions across complex systems in real time. Markov decision processes (MDPs) are the primary model for sequential decision problems with a large or indefinite time horizon. Choosing a representation of the underlying decision process that is both Markov and low-dimensional is non-trivial. We propose a method for constructing a low-dimensional representation of the original decision process for which: 1. the MDP model holds; 2. a decision strategy that maximizes mean utility when applied to the low-dimensional representation also maximizes mean utility when applied to the original process. We use a deep neural network to define a class of potential process representations and estimate the process of lowest dimension within this class. The method is illustrated using data from a mobile study on heavy drinking and smoking among college students.