This course is designed to provide graduate students in Electrical and Computer Engineering with a rigorous mathematical foundation for advanced topics in machine learning. It emphasizes the essential mathematical concepts required to understand and innovate in cutting-edge machine learning methods. The course focuses on two prominent areas: diffusion models and reinforcement learning, offering a deep exploration of their mathematical underpinnings and their role in state-of-the-art algorithms.
Students will develop the ability to analyze and solve complex problems by connecting theoretical mathematics with practical machine learning applications. The course also includes reading and discussing research papers, enabling students to understand how mathematical principles are applied in advanced research.
Acknowledgment of Sources
These slides include materials adapted from various publicly available slide decks uploaded by Nan Jiang(UIUC), Chi Jin(Princeton), Wen Sun(Cornell), and David Silver. I sincerely thank the original authors for their contributions to advancing education. Wherever possible, proper attribution has been provided on the relevant slides. If any source has been inadvertently omitted, please contact me, and I will make the necessary corrections.
Markovian Decision Processes and Bellman Equation (Slides incorporates materials from W.S. and N.J.)
Value Iteration (Slides incorporates materials from W.S.)
Policy Iteration and Linear Programming (Slides incorporates materials from W.S.)
Sample Complexity with Generative Models (Slides incorporates materials from W.S.)
Monte Carlo Method (Slides incorporates materials from H.W. and D.S.)