In this dissertation, we aim to develop a theoretical understanding of foundation models and reinforcement learning. We delve into a comprehensive analysis of specific aspects within these domains. The focal points of our study are as follows: • Generative Adversarial Imitation Learning (GAIL) with Neural Networks: GAIL is poised to...
Derivative-free optimization (DFO) has received growing attention due to important problems arising in practice. Various research communities, ranging from machine learning to engineering design, have adopted distinct DFO methods. In this thesis, we present extensive studies as a meaningful step towards a comprehensive understanding of DFO methods. We study the...
Submodularity is a well-known concept in integer programming and combinatorial optimization. Submodular set functions capture the diminishing returns phenomenon, which has wide-ranging applications in various domains. Typically, a submodular set function models the utility of homogenous items selected from a single ground set. Selecting an item or not is naturally...
This dissertation presents novel advancements in the field of continuous nonlinear optimization, focusing on the development of efficient second-order methods for second-order conic programs (SOCPs) and continuous nonlinear two-stage optimization problems. The primary focus is on the theory and computations of Sequential Quadratic Programming (SQP) methods, which are widely used...
Volunteers play an essential role in humanitarian and non-profit organizations that strive to improve society. 30% of the population in the United States volunteered in 2019, and this percentage has been stable for the past two decades. This dissertation is motivated by the scheduling decision process in nonprofit organizations. These...
This dissertation studies the integration of analytical modeling and optimization, machine learning, and Bayesian learning to optimize cost, access, and quality of healthcare delivery. Chapter 1 models computer-aided triage (patient prioritization) as feature-based priority queuing where types (diseases) are not perfectly observed but are inferred from observed features using a...
For stochastic simulation optimization in a modern computing era, we introduce a new parallel framework for solving very large-scale problems using a ranking & selection (R&S) approach that simulates all systems or feasible solutions to provide a global statistical guarantee. We propose a parallel adaptive survivor selection (PASS) framework that...
This dissertation contains three essays that study the operational challenges in healthcare-related fields. We strive to integrate analytical modeling and empirical methods to study decision-making under uncertainty for practice- and data-driven problems. We use large-scale datasets (millions) gathered from years of data collection. To gain access to these proprietary data,...
Market growth is an important goal for consumer businesses, often leading to lower marginal cost, higher operational efficiency, and larger assortment size - all of which help achieve dominance over competition. Yet, retailers and manufacturers alike should carefully manage their supply chains to sustain growth in customer base and extract...
Travel time is a key aspect of capturing and evaluating the operational performance and service quality of transportation systems, and travel time improvement is a common objective for travelers, service providers, transportation practitioners and agencies. However, the reliability of travel times, including the probability of unexpected delays, is an important...
