2024 Theses Doctoral

Distributional robustness and machine learning methods for stochastic decision-making

Zeng, Yibo

Recently, data-driven methods are increasingly shaping decision-making across domains such as classification, prediction, optimization, and resource allocation. While machine learning advancements have been pivotal, current models can be insufficient to handle unseen uncertainties from future data or new application domains, leading to unreliable decisions and performance risks. This thesis explores how distributionally robust methods can be combined with modern machine learning techniques to ensure more reliable decision-making. We develop new theoretical results and achieve state-of-the-art empirical results in three areas: generalization bounds in machine learning, queue scheduling with prediction errors, and tabular classification under 𝑌|𝑋 shifts.

The work is organized into three chapters. In Chapter 2, we derive novel generalization bounds for distributionally robust optimization (DRO). Our analysis implies generalization bounds whose dependence on the hypothesis class appears the minimal possible: The bound depends solely on the true loss function, independent of any other candidates in the hypothesis class. To our best knowledge, it is the first generalization bound of this type in the literature. Chapter 3 investigates optimal scheduling in service systems with prediction errors. We develop a near-optimal index-based policy that incorporates predicted class information. Our results guide model selection with a focus on downstream queueing performance and offer insights into designing queueing systems with AI-based triage. In Chapter 4, we study tabular data classification under 𝑌|𝑋 shift. We not only build a large-scale testbed, but also demonstrate that large language model (LLM) embeddings significantly improve classification performance, even with few labeled samples from the target domain.