OPERATIONS RESEARCH POWERED APPROACHES TO SEVERAL MACHINE LEARNING PROBLEMS

Abstract

Adoption of Machine Learning (ML) methods peaked in recent years due to increased hardware capacity and popularity of Large Language Models (LLMs). Although one of the most prominent aspects of ML is automating decisions and systems, this dissertation demonstrates that it is possible to improve ML algorithms using insights and methods from Operations Research. In the first essay, in the first part, we consider the problem of optimizing a black-box function using only pairwise comparison feedback. We model the black-box function as a Gaussian Process and develop a functional approximate inference mechanism to map preference feedback to artificial observations. In the second part, observing that our update mimics a gradient-descent step in the Reproducing Kernel Hilbert Space (RKHS), we show that the gradient-descent algorithm in RKHS solves an Empirical Risk Minimization (ERM) problem. Under some conditions, we show that the solution of the ERM problem recovers the minimizer of the unknown function. In the second essay, we consider alignment of generative models to preference feedback. In the first part, we develop the tDPO algorithm to incorporate the magnitude of preferences obtained from users. Our tDPO algorithm incorporates external predefined reward functions via a thresholding mechanism to determine the magnitude of observed preferences, enabling directed alignment without reward over-optimization. We empirically show that our method improves over baseline methods. In the second part, we propose ImParAlign, a multi-objective contextual bandit framework for efficient model selection across preference dimensions, where each arm represents a specialized model and contexts are input prompts. We introduce Bernoulli subsampling to reduce reward evaluation costs while maintaining unbiased estimates, and a weak-to-strong guided generation strategy where lightweight specialists guide a large base model via chunk-level beam search, eliminating the need for multiple large models. Experiments on multi-objective benchmarks demonstrate that our method achieves superior Pareto frontiers with substantially fewer trained models than baselines, making it practical for resource-constrained deployments. In the third essay, we consider dataset reduction for stochastic optimization. We decompose the reduction problem into two stages: subset selection and weight assignment. For subset selection, we introduce a k-NN Neighborhood Facility Location objective that generalizes the classical facility location function by extending the coverage radius of each selected point to its local k-nearest neighbor ball, and prove that this objective is normalized, monotone, and submodular, enabling a greedy algorithm with an approximation guarantee. Probability weights for the selected points are then assigned via optimal transport, yielding a reduced empirical measure that closely approximates the original data distribution. We establish finite-sample bounds on the expected Wasserstein distance between the reduced and full empirical measures, and connect our framework to the theory of k-nearest neighbor empirical processes to derive uniform convergence guarantees for the reduced empirical risk. Specifically, we show that any minimizer of the reduced empirical risk converges in probability to the minimizer of the true expected loss, and derive a closed-form optimal neighborhood size that balances approximation error against statistical bias. Computational experiments on deep learning benchmarks, mixed-integer programming for optimal classification trees, and synthetic datasets demonstrate that our method achieves substantial computational savings with predictable loss in solution quality. Overall, these three essays demonstrate the potential value of approaching ML problems with the tools of Operations Research.