Machine Learning under a Modern Optimization Lens

The objective of this mini-course is to present methodologies for integrating machine learning and optimization techniques. The use of optimization as a framework for predictive and prescriptive analytics is motivated by the significant advancement in high-performance computing and solvers for convex, linear, nonlinear, and integer optimization. On the predictive side, we will show how to formulate, solve, and extend classification and regression problems using mathematical programming instead of the traditionally used heuristic methods. In addition to the theoretical guarantees of optimality, the flexible optimization framework allows for the inclusion of features such as robustness and sparsity to achieve greater accuracy and better interpretability. On the prescriptive side, we will present the methodological advances that incorporate machine learning techniques into decision-making problems under uncertainty in the search for an optimal contextual decision. A new holistic end-to-end framework that processes data-to-decisions will be presented. We will illustrate these concepts with numerical experiments using various approaches presented in the literature.