Train faster, generalize better: Stability of stochastic gradient descent

TL;DR

This paper demonstrates that stochastic gradient methods with few iterations lead to models with vanishing generalization error, providing theoretical insights into why early stopping and training practices in neural networks are effective.

Contribution

It offers a unified stability-based analysis for both convex and non-convex optimization, explaining the generalization benefits of limited training epochs in deep learning.

Findings

SGM with few iterations has low generalization error.

Multiple epochs of training can still generalize well due to stability.

Popular deep learning training techniques promote stability and generalization.

Abstract

We show that parametric models trained by a stochastic gradient method (SGM) with few iterations have vanishing generalization error. We prove our results by arguing that SGM is algorithmically stable in the sense of Bousquet and Elisseeff. Our analysis only employs elementary tools from convex and continuous optimization. We derive stability bounds for both convex and non-convex optimization under standard Lipschitz and smoothness assumptions. Applying our results to the convex case, we provide new insights for why multiple epochs of stochastic gradient methods generalize well in practice. In the non-convex case, we give a new interpretation of common practices in neural networks, and formally show that popular techniques for training large deep models are indeed stability-promoting. Our findings conceptually underscore the importance of reducing training time beyond its obvious benefit.