Explore reinforcement learning through an optimization lens in this 47-minute lecture by Lihong Li from Google Brain. Delve into the fundamentals of reinforcement learning, including Markov Decision Processes, Bellman equations, and the challenges of online versus offline learning. Examine the intersection of Bellman and Gauss in approximate dynamic programming, and investigate a long-standing open problem in the field. Discover how linear programming reformulation and Legendre-Fenchel transformation address difficulties in solving fixed-point problems. Learn about a new loss function for solving Bellman equations and its eigenfunction interpretation. Conclude with practical applications using neural networks in a Puddle World scenario.