Decision-Dependent Distributionally Robust Markov Decision Process Method in Dynamic Epidemic Control

TL;DR

This paper introduces a robust decision-making framework for epidemic control that accounts for uncertainties in disease spread models, improving policy effectiveness and computational efficiency.

Contribution

The paper develops a novel decision-dependent distributionally robust MDP framework for epidemic control, with an efficient RTDP algorithm for scalable policy computation.

Findings

DRMDP reduces infection rates compared to classic MDP.

Proposed RTDP algorithm improves computational efficiency.

Robust approach handles transition uncertainties effectively.

Abstract

In this paper, we present a Distributionally Robust Markov Decision Process (DRMDP) approach for addressing the dynamic epidemic control problem. The Susceptible-Exposed-Infectious-Recovered (SEIR) model is widely used to represent the stochastic spread of infectious diseases, such as COVID-19. While Markov Decision Processes (MDP) offers a mathematical framework for identifying optimal actions, such as vaccination and transmission-reducing intervention, to combat disease spreading according to the SEIR model. However, uncertainties in these scenarios demand a more robust approach that is less reliant on error-prone assumptions. The primary objective of our study is to introduce a new DRMDP framework that allows for an ambiguous distribution of transition dynamics. Specifically, we consider the worst-case distribution of these transition probabilities within a decision-dependent ambiguity set. To overcome the computational complexities associated with policy determination, we propose an efficient Real-Time Dynamic Programming (RTDP) algorithm that is capable of computing optimal policies based on the reformulated DRMDP model in an accurate, timely, and scalable manner. Comparative analysis against the classic MDP model demonstrates that the DRMDP achieves a lower proportion of infections and susceptibilities at a reduced cost.