This lecture delves into optimization methods for training machine learning models, focusing on gradient descent and subgradients. The instructor explains the iterative process of minimizing loss functions using naive search, gradient descent, and stochastic gradient descent. The lecture covers the concept of subgradients for non-differentiable functions, providing insights into the linear models' optimization process. Additionally, the instructor introduces advanced optimization techniques like Adam optimization and discusses the importance of parallelization in optimizing large-scale models.