Gradient Descent: Proximal Operator and Step-Size Strategies

This lecture covers the concepts of proximal operator, gradient descent, and step-size strategies in the context of minimizing risk functions. It explains the derivation of the gradient-descent algorithm, the use of constant step-sizes, and the transition to iteration-dependent step-sizes. The lecture also discusses the convergence analysis under different step-size conditions, such as constant and vanishing step-sizes, and their impact on the convergence rate of the algorithm.