Learning with SGD and Random Features

TL;DR

This paper analyzes the use of stochastic gradient descent combined with random features for large-scale nonparametric learning, deriving finite sample bounds and illustrating their effectiveness through experiments.

Contribution

It provides a theoretical analysis of stochastic gradient methods with random features in nonparametric learning, including finite sample bounds and parameter insights.

Findings

Finite sample bounds for the estimator

Parameters like features, iterations, and batch size influence learning

Numerical experiments validate theoretical results

Abstract

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.