Event

 

Abstract:

This thesis develops methods in stochastic control and stochastic gradient estimation, with a focus on applications to kidney transplantation.

The first part studies the optimal acceptance of possibly incompatible kidneys for individual end-stage kidney disease patients. Incompatibility between donor and recipient is a key challenge in transplantation. To model its impact, we formulate a Markov Decision Process (MDP) that incorporates compatibility as a state variable. Under appropriate conditions, we prove the existence of control limit-type optimal policies that are both computationally efficient and practical to implement. Numerical experiments demonstrate the benefit of incorporating compatibility into decision-making, showing its influence on transplant outcomes.

The second part addresses simulation-based policy optimization for the transplantation problem. To enable gradient-based optimization, we develop a smoothed perturbation analysis (SPA) estimator. This is a Monte Carlo method for estimating the gradient of the MDP value function with respect to the control limit—the main decision variable. The estimator is asymptotically unbiased and applicable to value functions whose gradients cannot be expressed in explicit form.

The third part focuses on gradient estimation for general discontinuous sample performance functions. We propose a novel push-out Leibniz integration approach, which extends the conventional push-out likelihood ratio (LR) method. Unlike standard push-out LR, it allows the sample space to depend on parameters after a change of variables. The method remains valid even when the change of variables exists only locally. It also generalizes existing generalized likelihood ratio (GLR) estimators as special cases and applies to a broader class of discontinuous sample performance functions. By requiring weaker regularity conditions, it improves both applicability and ease of implementation.