Optimization Methods for Supervised Machine Learning: From Linear Models to Deep Learning
By Frank E. Curtis, Katya Scheinberg. 2017
47 citations recorded by the source corpus.
The goal of this tutorial is to introduce key models, algorithms, and open questions related to the use of optimization methods for solving problems arising in machine learning. It is written with an INFORMS audience in mind, specifically those readers who are familiar with the basics of optimization algorithms, but less familiar with machine learning. We begin by deriving a formulation of a supervised learning problem and show how it leads to various optimization problems, depending on the context and underlying assumptions. We then discuss some of the distinctive features of these optimization problems, focusing on the examples of logistic regression and the training of deep neural networks. The latter half of the tutorial focuses on optimization algorithms, first for convex logistic regression, for which we discuss the use of first-order methods, the stochastic gradient method, variance reducing stochastic methods, and second-order methods. Finally, we discuss how these approaches can be employed to the training of deep neural networks, emphasizing the difficulties that arise from the complex, nonconvex structure of these models.
Subfields: Artificial Intelligence, Optimization & Training
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Simon Lacoste-Julien
- Yoshua Bengio
- Andrea Lodi
- Sébastien Lachapelle
- Peter Richtárik
- Martin Jaggi
- Claudio Gambella
- Joe Naoum-Sawaya
In Optimization & Training
- Simon Lacoste-Julien
- Sébastien Lachapelle
- Yoshua Bengio
- Andrea Lodi
- Joe Naoum-Sawaya
- Bissan Ghaddar
- Eric Larsen
- Emma Frejinger
Citations in the corpus
- Predicting Tactical Solutions to Operational Planning Problems under Imperfect Information (2018, background): “The interested reader is referred to, e.g., Curtis and Scheinberg (2017) for a tutorial.”
- Optimization Models for Machine Learning: A Survey (2019, background): “While this survey does not discuss numerical optimization techniques since they were recently reviewed in [42, 76, 215], we note the fundamental role of the stochastic gradient algorithm [180] and its variants on large scale machine learning.”