MathFoundationRL/Book-Mathematical-Foundation-of-Reinforcement-Learning: what the repository actually ships
This is the homepage of a new book entitled "Mathematical Foundations of Reinforcement Learning."
At a glance
- What is it?
- The GitHub home of Zhao's Mathematical Foundations of Reinforcement Learning is a PDF distribution plus a MATLAB grid world, not a library. Here is what is in it, what it is not, and who it fits.
- Who is it for?
- Adopt it if you want a derivation-first RL text with a matching video course and a MATLAB grid world you can modify, and you already have probability and linear algebra. Do not adopt it if you need a maintained Python library or a pip-installable environment; the repository is a book companion, the code ships as a folder rather than a package, and no license file is listed at the top level.
- Can I use it commercially?
- Not without permission. GitHub finds no licence file in the repository, and without a licence all rights are reserved by default: you may read the code but not reuse it. Check the README, or ask the authors, before using it.
- Is it still maintained?
- Yes. The repository last received commits 1 day ago.
- What is it written in?
- Mainly MATLAB, according to GitHub's language statistics.
Answers come from the project's GitHub data, last synced on September 30, 2026, and from our analysis. They are not legal advice.
Editorial analysis
What the repository is, and who the book is written for
The README describes a book, not a software project. The repository is the book's homepage, and its job is to put the manuscript, the slides and the example code in one place. The stated readership is senior undergraduates, graduate students, researchers and practitioners. No prior reinforcement learning background is assumed, but probability theory and linear algebra are, and some of that background is repeated in the appendix.
The README is explicit about the angle: the book is "mathematical but friendly", and the aim is that readers understand why an algorithm was designed and why it works, not only the procedure. The author's framing is that the mathematics is deliberately capped at an adequate depth, and that readers can skip the gray boxes if they want a lighter pass. That is a real editorial choice with a cost: if you want a code-first tour, this is the wrong entry point.
How the material is organised: ten chapters, one grid world, two PDF tracks
The top-level directory listing shows the structure plainly. Each chapter exists as its own PDF, numbered 3 - Chapter 1 Basic Concepts.pdf through 3 - Chapter 10 Actor-Critic Methods.pdf, with separate files for the table of contents, an overview, the preface and the appendix. There is also a combined Book-all-in-one.pdf, and a file named 5 - Errata for the Springer version.pdf.
That last file matters more than its position suggests. It tells you the Springer edition and the repository PDFs are not assumed to be identical, and the README does not describe how the errata are applied or whether the chapter PDFs already incorporate them. If you cite a page number in a course, check which file you read it from.
The README splits the ten chapters into two parts: basic tools first, algorithms second, and it states that the chapters are highly correlated and generally should be studied in order. Every example in the book is built on a single grid world task. That is a deliberate simplification, and it is also the main limitation: the grid world keeps the derivations legible, but it does not exercise function approximation at the scale a practitioner meets in production.
Getting the book and running the grid world code
There is no install step, no package and no command line tool. The README points to the publisher page for the Springer edition, and the repository itself carries the PDFs. Downloading the repository is the whole setup for reading:
git clone https://github.com/MathFoundationRL/Book-Mathematical-Foundation-of-Reinforcement-Learning.git
cd Book-Mathematical-Foundation-of-Reinforcement-Learning
lsThe listing should show the numbered chapter PDFs, Book-all-in-one.pdf, the Errata file, and the directories Code for grid world, Lecture slides and Readme_Images. The README does not give a per-file description of the code folder, so read the scripts before running them.
For the code, the primary language of the repository is MATLAB. The README gives no run instructions, no required toolbox list and no version. The practical path is to open the folder in MATLAB and run a script from there:
cd('Code for grid world')
lsWhat you see after that depends on the contents of the folder, which the README does not enumerate. Treat the scripts as illustrative implementations that match the book's examples, not as a validated environment you can rely on for experiments.
If you want the lectures alongside the text, the README links a Chinese track on Bilibili and YouTube, and an English track on YouTube, including an "Overview of Reinforcement Learning in 30 Minutes" video and per-lecture videos for L1 through L5 and beyond. The README states the lecture videos have received 2,100,000+ views. That is a reach figure, not a measure of correctness.
Where this repository stops being the right tool
The slides are the clearest example of a boundary the README draws itself. It says the slides were created with Latex/Beamer, and that a professor preparing a course can email the author to ask for the source. The source is not in the repository. If your workflow depends on editing the slides rather than presenting them, you are dependent on a reply, and the README warns that due to a high volume of commitments there may be significant delays in responses to reader feedback and questions in the discussion section.
There is a second boundary in the code. The repository language is MATLAB, so anyone working in Python has to port the examples rather than import them. Nothing in the README describes a Python package, a Gymnasium environment, or an installable artifact, and there are no releases. The grid world is a teaching device: small state spaces, tabular values, and derivations you can check by hand. It will not tell you anything about sample efficiency or stability in a continuous control setting.
Finally, the license is not identified in the repository metadata supplied here. The README mentions sharing slide source by email but says nothing about reuse terms for the PDFs or the code. That is a genuine gap, not a detail.
How it compares with Sutton and Barto
The obvious alternative is Reinforcement Learning: An Introduction by Sutton and Barto, which is also distributed as a free PDF and is the default reference in the field. The difference is in the ordering of the argument. Sutton and Barto build intuition and breadth first, moving through bandits, dynamic programming, temporal-difference learning and function approximation with a lot of informal reasoning along the way.
This book inverts that. The README's stated goal is to introduce reinforcement learning from a mathematical point of view, to explain why an algorithm was designed and why it works, and to keep the mathematics at a controlled depth. The chapters are sequenced as tools first and algorithms second, with each chapter built on the preceding one, so the reader is expected to move linearly rather than sample topics. The single grid world example is used throughout, which makes the book more internally consistent than a survey text and narrower in the situations it covers.
Neither is a library. If what you actually need is a maintained implementation of these algorithms, neither book repository is the answer, and you should be looking at an RL framework instead.
Maintenance, licensing and what a course would have to absorb
The repository is not archived, and the last push was on 2026-09-21. There are no tagged releases, so there is no version to pin and no changelog to read. Upgrades arrive as commits to PDFs and to the code folder, which means a course that cites page numbers has to recheck them after a pull. The Errata for the Springer version file exists precisely because the printed and repository versions can diverge, and the README does not explain the reconciliation process.
The license is unknown from the repository metadata. The README offers slide source to professors on request, which implies the author is willing to share for teaching, but that is a sentence in a README and not a licence grant. If you plan to redistribute the PDFs, reuse figures in your own materials, or ship the MATLAB code inside a product, resolve the terms with the author or the publisher first. Nothing here is legal advice, and the absence of a LICENSE file is the fact you have to act on.
Cost of adoption is mostly reading time. The README says probability and linear algebra are prerequisites, with basics repeated in the appendix, and that the gray boxes are optional. A reader who skips the gray boxes and the derivations is left with a shorter book than the table of contents suggests.
Editorial conclusion
Adopt it if you want a derivation-first RL text with a matching video course and a MATLAB grid world you can modify, and you already have probability and linear algebra. Do not adopt it if you need a maintained Python library or a pip-installable environment; the repository is a book companion, the code ships as a folder rather than a package, and no license file is listed at the top level. Verify the licence terms and the Errata PDF before you build a course around it, and check whether the Springer chapter PDFs or the Book-all-in-one.pdf is the version you intend to cite.
Frequently asked questions
What is the best book to learn about reinforcement learning?
The README positions this book as a mathematical but friendly introduction aimed at senior undergraduates, graduate students, researchers and practitioners, and says no prior reinforcement learning background is required. It does require probability theory and linear algebra, with some basics repeated in the appendix.
What are some recommended books for learning about reinforcement learning?
The repository only documents its own book, Mathematical Foundations of Reinforcement Learning by S. Zhao, published by Springer Press. It does not list or compare other titles, so it offers no recommendation beyond itself.
Is RL the future of AI?
The README does not make predictions about the field. It describes the scope of the book, the ten chapters split into basic tools and algorithms, and the grid world used for every example, and leaves the question of where reinforcement learning is heading open.
What is the math behind reinforcement learning?
The README says the book introduces reinforcement learning from a mathematical point of view so readers understand why an algorithm was designed and why it works, with the mathematics held at a controlled depth. Probability theory and linear algebra are the stated prerequisites, and the appendix repeats some of the required basics.
Official sources
Add this badge to your README
If you maintain this project, the badge below links readers to this analysis and shows its maintenance status from the daily GitHub snapshot. Paste the markdown into your README; add ?metric=license or ?metric=stars to the image URL for a different field.
[](https://hysenlabs.com/projects/mathfoundationrl-book-mathematical-foundation-of-reinforcement-learning)