Explore the statistical complexities of reinforcement learning in this 47-minute lecture by Mengdi Wang from Princeton University. Delve into key theoretical questions surrounding RL, including sample complexity, regret analysis, and off-policy evaluation. Examine recent findings on minimax-optimal sample complexities for solving Markov Decision Processes, optimal off-policy evaluation through regression, and regret bounds for online RL with nonparametric model estimation. Gain insights into tabular MDPs, state feature mapping, Bellman equation reduction, and episodic reinforcement learning. Understand the importance of feature space embedding of transition kernels and exploration techniques like Value-Targeted Regression. This talk, part of the Intersections between Control, Learning and Optimization 2020 series at the Institute for Pure & Applied Mathematics, offers a comprehensive overview of recent advancements in the theoretical foundations of reinforcement learning.