Stochastic Gradient Descent: Optimization and Convergence

This lecture covers the optimality of convergence rate, acceleration, and the application of stochastic gradient descent in optimization problems. Starting with the basics of gradient descent, the instructor explains the iterative process and convergence criteria. The lecture then delves into stochastic gradient descent (SGD), detailing its implementation, advantages, and convergence properties. Various scenarios, including convex and non-convex problems, are discussed, along with the impact of step sizes on convergence rates. The presentation also explores practical examples, such as convex optimization with finite sums and synthetic least-squares problems. Additionally, the lecture introduces advanced topics like SGD variants, SGD with averaging, and adaptive methods for stochastic optimization, providing insights into their applications and convergence guarantees.