2025 Theses Doctoral

Scalable Approaches in Optimization, Preference Modeling, and Predictive Simulation for Decision-Making

Chen, Haoxian

In an era where data-driven decisions increasingly influence high-stakes outcomes, from financial risk assessment and healthcare resource allocation to AI model alignment, the demand for algorithms that are both statistically principled and computationally scalable has become increasingly urgent. Classical methods grounded in probabilistic modeling and statistical inference offer strong theoretical guarantees, including unbiasedness, consistency, and well-calibrated uncertainty estimates. However, these methods often struggle to adapt to the scale, complexity, and heterogeneity of modern machine learning tasks. In contrast, contemporary machine learning models are highly expressive and flexible, but frequently lack transparency, reliability, and rigorous control over uncertainty.

This thesis aims to bridge this divide by developing hybrid frameworks that integrate the scalability and adaptability of modern machine learning with the foundational strengths of statistical methodology, preserving properties such as unbiasedness, (local) consistency, and uncertainty quantification while enabling practical performance across complex real-world applications. The work spans three major threads: black-box optimization, preference-based fine-tuning, and simulation-based evaluation.

In Chapter 2, we propose Pseudo-Bayesian Optimization (PseudoBO), a general-purpose framework for black-box optimization that extends beyond Gaussian processes. By decomposing exploration-based black-box optimization algorithms into modular surrogate predictors, uncertainty quantifiers, and acquisition functions, and formalizing their interaction via a set of axioms, PseudoBO provides convergence guarantees for a wide class of functions using non-Bayesian models such as neural networks and local regressors.

In Chapter 3, we introduce MallowsPO, a novel generalization of Direct Preference Optimization (DPO) that explicitly accounts for heterogeneity in human preferences through dispersion modeling. By leveraging Mallows ranking theory, MallowsPO adapts the training objective of language models based on how consistently users agree on different types of prompts, enhancing robustness, generalization, and controllability in LLM alignment tasks.

In Chapter 4, we develop Prediction-Enhanced Monte Carlo (PEMC), a hybrid estimation method that combines cheap, parallelizable simulation features with machine-learned predictors to reduce variance while preserving unbiasedness and valid confidence intervals. PEMC offers a drop-in enhancement to classical Monte Carlo workflows, demonstrating substantial runtime and sample efficiency gains across domains such as ambulance diversion policies evaluation and exotic financial derivative pricing.

Taken together, these contributions advance a new paradigm in statistical machine learning that embraces a stronger interplay between predictive modeling and uncertainty quantification. By designing learning-augmented algorithms that remain grounded in theoretical rigor, this thesis lays the foundation for more trustworthy, scalable, and efficient decision-making systems in uncertain and high-stakes environments.