Scalable Optimization for Interpretable Machine Learning

Machine learning is increasingly used in fields such as finance and medical care, where decisions need to be accurate and understandable. Many high-performing models act as black boxes, providing little insight into how predictions arise. This project approaches interpretability through mathematical optimization, combining transparent model structure with efficient computation. The research expresses interpretable machine-learning problems in a unified framework as quadratic optimization with complementarity constraints. This mathematical formulation captures the logical relationships that determine a models decisions, for example, which features are active or inactive in a prediction. To make these complex models computationally manageable, the project first exploits sparsity patterns in their structure and reformulates them as compact convex problems in a higher-dimensional space. These higher-dimensional representations are then relaxed into tight yet tractable convex approximations that preserve the key properties of the original models while enabling efficient solution. The resulting convex relaxations are solved using first-order decomposition methods that scale well to large datasets. These algorithms are integrated into a structure-aware branch- and-bound framework, which uses the relaxations to guide the search toward globally optimal solutions. By uniting rigorous modeling with scalable numerical methods, the project builds a bridge between optimization theory and interpretable machine learning. The resulting open- source tools and case studies will demonstrate how mathematical optimization can make data-driven decisions more transparent, reliable, and efficient.