Policy Iteration and Linear Programming in MDPs

This lecture covers the concepts of policy iteration and linear programming in the context of Markov Decision Processes (MDPs). It begins with the Policy Improvement Theorem, which establishes the relationship between deterministic policies and their value functions. The instructor explains how policy iteration involves evaluating a policy and then improving it iteratively until no changes occur. The lecture emphasizes the importance of the Bellman operator and its contractive properties, leading to optimal solutions in infinite horizon settings. The discussion then transitions to linear programming as an alternative method for solving MDPs, detailing how to formulate the problem of finding optimal values as a linear program. The instructor provides examples to illustrate the application of these concepts, including maximizing future discounted values and reward rates. The lecture concludes with a summary of key points, reinforcing the connection between dynamic programming and linear programming approaches in MDPs.