Stochastic Gradient Descent: Non-convex Optimization Techniques

This lecture covers Stochastic Gradient Descent (SGD) and its application in non-convex optimization. It begins with an introduction to SGD, explaining its efficiency in handling sum-structured objective functions, where the cost function is derived from multiple observations. The instructor details the algorithm, emphasizing the benefits of using stochastic gradients over full gradients, which significantly reduces computational costs. The lecture further explores the concept of unbiasedness in stochastic gradients and presents theorems regarding convergence rates under various conditions, including bounded stochastic gradients and strong convexity. The discussion extends to mini-batch SGD, highlighting its advantages in variance reduction and parallelization. The lecture also addresses challenges in non-convex optimization, such as local minima and saddle points, and introduces concepts of smooth functions and bounded Hessians. Finally, the instructor discusses the implications of these techniques in machine learning, providing a comprehensive understanding of optimization strategies in complex scenarios.