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arXiv · 1810.08102

First-order and second-order variants of the gradient descent in a unified framework

Thomas Pierrot·Nicolas Perrin·Olivier Sigaud
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Abstract

In this paper, we provide an overview of first-order and second-order variants of the gradient descent method that are commonly used in machine learning. We propose a general framework in which 6 of these variants can be interpreted as different instances of the same approach. They are the vanilla gradient descent, the classical and generalized Gauss-Newton methods, the natural gradient descent method, the gradient covariance matrix approach, and Newton's method. Besides interpreting these methods within a single framework, we explain their specificities and show under which conditions some of them coincide.

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Thomas Pierrot, Nicolas Perrin, Olivier Sigaud. 2018-10-18. First-order and second-order variants of the gradient descent in a unified framework. https://arxiv.org/abs/1810.08102

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