mathfoundationrl/book-mathematical-foundation-of-reinforcement-learning

This repository is the homepage of a textbook called "Mathematical Foundations of Reinforcement Learning" by S. Zhao, published by Springer Press in 2025. It is not a software project, the repo hosts the book's promotional material, lecture slides, accompanying code in MATLAB, and links to free lecture videos. Reinforcement learning is the branch of artificial intelligence concerned with how an agent learns to act in an environment by trying things, getting rewards or penalties, and gradually figuring out a strategy that works. The book gives a mathematical but friendly introduction to the fundamental concepts, basic problems, and classic algorithms. The author's goal is that readers not only know how an algorithm works step by step, but understand why it was designed that way. The depth of the mathematics is deliberately controlled, with optional deeper material set aside in grey boxes, and every concept is illustrated using a recurring "grid world" task so examples stay easy to follow. The ten chapters split into two parts, basic tools first, then algorithms. You would reach for this book if you are a senior undergraduate, graduate student, researcher or practitioner who wants to learn reinforcement learning from first principles. It does not assume prior knowledge of the field, but expects comfort with probability theory and linear algebra, a short appendix covers the necessary mathematics. The author has taught a graduate-level course since 2019 and the book grew out of those lecture notes. The companion lecture videos, in English and Chinese, have over 2,100,000 views across YouTube and Bilibili, and the slides themselves are built with LaTeX/Beamer.