PhD Course: Mathematical Optimization for Machine Learning - Foundations

Behind every successful machine learning model lies an optimization problem. While algorithms are the engines of learning, the mathematical modeling of the objective function determines a model's ability to generalize, scale, and remain interpretable. In this 8-hour course, we transition from the basic calculus to the sophisticated optimization structures that define modern learning models. We begin by reviewing mathematical background in optimality conditions and duality, providing the toolkit to understand how machine learning tasks are translated into formal optimization problems. After a brief overview on the most used strategy for solving optimization problems, we explore how specific mathematical formulations drive model behavior. Key highlights include the analysis of Support Vector Machines (SVMs) through the lens of soft-margin formulations and the kernel trick; the use of sparsity to select features, leveraging the L0-pseudo-norm and k-norms; the nonlinear separability framework, i.e., those optimization models for separation that are based on nonlinear surfaces; the optimization models tailored for semi-supervised learning environments.

2CFU

• lunedì 25 maggio, ore 14:00-17:00 - aula 43B3 (Cubo 43B, Piano ponte carrabile)
• martedì 26 maggio, ore 10:30-13:30 - aula DS6 (Cubo 41B, 2° Piano)
• mercoledì 27 maggio, ore 15:00-17:00 - aula 43B3 (Cubo 43B, Piano ponte carrabile)