Optimization Methods in Machine Learning

This lecture delves into optimization methods in machine learning, focusing on gradient descent and stochastic gradient descent. The instructor explains the importance of understanding gradients, costs, and computational efforts in optimization. The lecture covers topics such as full gradient computation, individual element gradients, subgradients, and convexity. Additionally, the instructor discusses the concept of subgradients for non-differentiable functions and the use of penalties to encourage sparsity in models. The lecture also touches on optimality conditions, step size selection, and preconditioning to improve optimization performance.