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.
