The mathematical theory of machine learning not only explains the current algorithms but can also motivate principled approaches for the future. This self-contained textbook introduces students and researchers of AI to the main mathematical techniques used to analyze machine learning algorithms, with motivations and applications. Topics covered include the analysis of supervised learning algorithms in the iid setting, the analysis of neural networks (e.g. neural tangent kernel and mean-field analysis), and the analysis of machine learning algorithms in the sequential decision setting (e.g. online learning, bandit problems, and reinforcement learning). Students will learn the basic mathematical tools used in the theoretical analysis of these machine learning problems and how to apply them to the analysis of various concrete algorithms. This textbook is perfect for readers who have some background knowledge of basic machine learning methods, but want to gain sufficient technical knowledge to understand research papers in theoretical machine learning.

Provides a self-contained, systematic treatment of theoretical machine learning, allowing students to learn the subject in a comprehensive and systematic way
Serves as a reference for many useful results normally scattered among different publications
Readers learn how to apply newly learned tools and algorithms to concrete machine learning methods
Focuses on the analysis of two common learning models – supervised learning and online learning – and covers all key ideas, including the recent analysis of neural networks.