Training machine learning models often involves datasets that are too large to process in a single batch. Standard gradient descent, which requires computing the gradient over the entire dataset, becomes computationally infeasible. While Stochastic Gradient Descent (SGD) provides a scalable alternative by using gradients from small data samples (mini-batches), this introduces significant variance into the optimization process, potentially slowing down convergence.

This chapter addresses the specific challenges of optimizing models with massive datasets. You will learn about:

• Variance Reduction Techniques: Methods like Stochastic Average Gradient (SAG) and Stochastic Variance Reduced Gradient (SVRG) that aim to accelerate convergence by reducing the noise inherent in stochastic gradients.
• Mini-batch Gradient Descent Analysis: Understanding the practical trade-offs associated with choosing different mini-batch sizes.
• Parallel and Distributed Strategies: Concepts like asynchronous SGD and data parallelism that distribute the computational load across multiple processors or machines.

We will examine how these techniques allow for efficient training on datasets that would otherwise be intractable. Practical implementations and the analysis of their convergence behavior will be key components.