Bridging Machine Learning and Optimization: Learning Fair and Scalable Problem Solving

This thesis explores the integration of Machine Learning (ML) and Optimization through two frameworks: Predict-Then-Optimize (PtO) and Learning to Optimize (LtO), with a focus on enhancing fairness, scalability, and efficiency in complex decision-making systems. The PtO framework integrates ML and optimization by incorporating the optimization layer directly into the ML training process. Our contributions in this area focus on multi-objective optimization applications, including learning-to-rank, court scheduling, and portfolio management. By integrating optimization layers into ML models, we address challenges such as fairness and risk management, leading to more robust and effective decision-making processes. The LtO framework utilizes ML models, particularly neural networks, to accelerate the solution of constrained optimization problems. We demonstrate its application in power systems, specifically for the AC Optimal Power Flow problem, where our approach significantly reduces computational costs while maintaining high accuracy and low constraint violation. Additionally, we investigate a hybrid of PtO and LtO by learning surrogate models for intractable Mixed-Integer Programming (MIP) problems in an end-to-end framework, illustrated through a court scheduling application. These studies highlight the potential of combining both domains to enhance real-world problem-solving capabilities.