Decision-Dependent Distributionally Robust Markov Decision Process Method in Dynamic Epidemic Control
This addresses the problem of robust decision-making in epidemic management for public health, but it is incremental as it builds on existing MDP and distributionally robust optimization methods.
The paper tackles dynamic epidemic control by introducing a Distributionally Robust Markov Decision Process (DRMDP) framework that accounts for ambiguous transition probabilities, and it shows that DRMDP achieves a lower proportion of infections and susceptibilities at reduced cost compared to classic MDP.
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.