Optimization Methods for Large-Scale Machine Learning

The paper provides a review and commentary on the past, present, and future of numerical optimization algorithms in the context of machine learning applications. Through case studies on text classification and the training of deep neural networks, it discusses how optimization problems arise in machine learning and what makes them challenging, arguing that large-scale machine learning is a distinctive setting in which the stochastic gradient (SG) method has traditionally played a central role while conventional gradient-based nonlinear optimization techniques typically falter.

Building on this viewpoint, the authors present a comprehensive theory of a straightforward yet versatile SG algorithm, discuss its practical behavior, and highlight opportunities for designing algorithms with improved performance. This leads to a discussion of the next generation of optimization methods for large-scale machine learning, including two main streams of research: techniques that diminish noise in the stochastic directions and methods that exploit second-order derivative approximations.