Proposal Exam: Xingyu Ren
Wednesday, September 27, 2023
301 405 3681
ANNOUNCEMENT: Ph.D. Research Proposal Exam
Name: Xingyu Ren
Professor Michael C. Fu (Chair)
Professor Steven I. Marcus
Professor P. S. Krishnaprasad
Date/time: Wed Sep 27, 2023 at 3pm
Title: Optimal stopping of Markov decision processes with application to organ transplantations
Incompatibility between a patient and a donor is a significant obstacle in kidney transplantation (KT). The increasing shortage of kidney donors has driven the development of desensitization techniques to overcome this immunological challenge. Compared with compatible KT, patients undergoing incompatible KTs are more likely to experience rejection, infection, malignancy, and graft loss.
The research proposal presents a Markov Decision Process (MDP) model to formulate the individual organ acceptance decision process as a stochastic control problem. Under the umbrella of the MDP framework, we classify and summarize the major research streams and contributions. In particular, we focus on control limit-type policies, which are shown to be optimal under certain conditions and easy to implement in practice.
To capture the effect of incompatibility, we propose an MDP model that explicitly includes compatibility as a state variable. The resulting higher-dimensional model makes it more challenging to analyze, but under suitable conditions, we establish the existence of control limit-type optimal policies. Additionally, to estimate the gradient of the total expected discounted reward with respect to the control limit, we examine techniques for stochastic gradient estimation and explore the implementation of the smoothed perturbation analysis (SPA) estimator and generalized likelihood ratio (GLR) estimator.
Finally, some open research questions are presented, including the existence of a control limit optimal policy under the framework of a risk-sensitive MDP and/or an MDP with a multidimensional state space.