Optimization Methods for Supervised Machine Learning: From Linear Models to Deep Learning

摘要

The goal of this tutorial is to introduce key models, algorithms, and openquestions related to the use of optimization methods for solving problemsarising in machine learning. It is written with an INFORMS audience in mind,specifically those readers who are familiar with the basics of optimizationalgorithms, but less familiar with machine learning. We begin by deriving aformulation of a supervised learning problem and show how it leads to variousoptimization problems, depending on the context and underlying assumptions. Wethen discuss some of the distinctive features of these optimization problems,focusing on the examples of logistic regression and the training of deep neuralnetworks. The latter half of the tutorial focuses on optimization algorithms,first for convex logistic regression, for which we discuss the use offirst-order methods, the stochastic gradient method, variance reducingstochastic methods, and second-order methods. Finally, we discuss how theseapproaches can be employed to the training of deep neural networks, emphasizingthe difficulties that arise from the complex, nonconvex structure of thesemodels.