On the Benefits of Large Learning Rates for Kernel Methods - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2022

On the Benefits of Large Learning Rates for Kernel Methods


This paper studies an intriguing phenomenon related to the good generalization performance of estimators obtained by using large learning rates within gradient descent algorithms. First observed in the deep learning literature, we show that such a phenomenon can be precisely characterized in the context of kernel methods, even though the resulting optimization problem is convex. Specifically, we consider the minimization of a quadratic objective in a separable Hilbert space, and show that with early stopping, the choice of learning rate influences the spectral decomposition of the obtained solution on the Hessian's eigenvectors. This extends an intuition described by Nakkiran (2020) on a two-dimensional toy problem to realistic learning scenarios such as kernel ridge regression. While large learning rates may be proven beneficial as soon as there is a mismatch between the train and test objectives, we further explain why it already occurs in classification tasks without assuming any particular mismatch between train and test data distributions.
Fichier principal
Vignette du fichier
beugnot22a.pdf (645.18 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03878527 , version 1 (29-11-2022)


  • HAL Id : hal-03878527 , version 1


Gaspard Beugnot, Alessandro Rudi, Julien Mairal. On the Benefits of Large Learning Rates for Kernel Methods. COLT 2022 - 35th Annual Conference on Learning Theory, Jul 2022, London, United Kingdom. pp.254--282. ⟨hal-03878527⟩
34 View
17 Download


Gmail Facebook Twitter LinkedIn More