Policy Gradient Methods: Convergence and Optimization

This lecture discusses the convergence of policy gradient methods in reinforcement learning, focusing on key questions such as when these methods converge to optimal solutions and the speed of convergence. The instructor revisits the performance difference lemma, which compares cumulative rewards of different policies, and explains the significance of the state visitation distribution in this context. The lecture also covers the advantages of using natural policy gradients and the implications of advantage estimation for convergence. The instructor emphasizes the convex-like nature of policy optimization and introduces the projected policy gradient method, detailing its iterative process and convergence guarantees. Additionally, the lecture explores the relationship between policy optimization and the Fisher information matrix, highlighting the importance of understanding the geometry of the policy space. The session concludes with a discussion on the challenges of exploration in reinforcement learning and the necessity of offline policy evaluation and optimization.