This thrust focuses on applying optimization to speed up machine learning algorithms. Optimization algorithms, e.g., stochastic gradient algorithms, play a key role in training machine learning models. The thrust studies how to improve these algorithms, reduce their computational requirements, and capture important requirements with more fidelity. In particular, the thrust proposed novel optimization methods to impose sparsity in learning models, a fundamental feature for explainability. AI4OPT also devotes attention to learning models concerned with combinatorial objects. The thrust has shown that flow algorithms may be of significant benefits to a variety of learning tasks.