Learning with SGD and Random Features

Luigi Carratino (1) , Alessandro Rudi (2, 3, 4) , Lorenzo Rosasco (1, 5)

1 DIBRIS - Dipartimento di Informatica, Bioingegneria, Robotica e Ingegneria dei Sistemi [Genova]
2 PSL - Université Paris Sciences et Lettres
3 DI-ENS - Département d'informatique - ENS Paris
4 SIERRA - Statistical Machine Learning and Parsimony
5 IIT - Istituto Italiano di Tecnologia

Sketching and stochastic gradient methods are arguably the most common techniques to derive efficient large scale learning algorithms. In this paper, we investigate their application in the context of nonparametric statistical learning. More precisely, we study the estimator defined by stochastic gradient with mini batches and random features. The latter can be seen as form of nonlinear sketching and used to define approximate kernel methods. The considered estimator is not explicitly penalized/constrained and regularization is implicit. Indeed, our study highlights how different parameters, such as number of features, iterations, step-size and mini-batch size control the learning properties of the solutions. We do this by deriving optimal finite sample bounds, under standard assumptions. The obtained results are corroborated and illustrated by numerical experiments.

Domaines: Apprentissage [cs.LG]

Luigi Carratino, Alessandro Rudi, Lorenzo Rosasco. Learning with SGD and Random Features. Advances in Neural Information Processing Systems, Dec 2018, Montreal, Canada. pp.10213--10224. ⟨hal-01958906⟩