Lecture
This lecture covers the fundamentals of Markov Decision Processes (MDPs) and their applications in dynamic programming. It begins with an introduction to Q-values and the significance of MDPs in defining Markov chains with time-dependent transition probabilities. The instructor discusses the Cliff-Walking MDP exercise, emphasizing the importance of understanding absorbing states and their implications for policy formulation. The lecture then delves into fixed-point iterations and Banach's Fixed Point Theorem, illustrating how these concepts can be applied to solve equations iteratively. The Bellman operator is introduced as a key mapping in MDPs, which allows for the computation of optimal policies through value iteration. The process of maximizing future discounted values is explained, highlighting the convergence of the Bellman operator to a unique fixed point. The lecture concludes with a discussion on the characteristics of optimal policies, emphasizing their deterministic and stationary nature in infinite horizon scenarios, and introduces value iteration as a practical algorithm for solving MDPs.