Explore the intricacies of policy gradient methods in Markov Decision Processes through this 55-minute lecture by Alekh Agarwal from Microsoft Research Redmond. Delve into optimality and approximation concepts as part of the "Emerging Challenges in Deep Learning" series at the Simons Institute. Examine MDP preliminaries, policy parameterizations, and the policy gradient algorithm, with a focus on softmax parameterization and entropy regularization. Analyze the convergence of entropy-regularized PGA, natural solutions, and proof ideas. Investigate restricted parameterizations, natural policy gradient updates, policy assumptions, and extensions to finite samples. Gain valuable insights into this crucial area of deep learning and reinforcement learning research.