Beyond Implicit Bias: The Insignificance of SGD Noise in Online Learning

TL;DR

This paper investigates the role of SGD noise in online learning, finding that small batch sizes do not induce implicit bias benefits but mainly offer computational advantages, challenging previous beliefs.

Contribution

The study provides empirical evidence that SGD noise does not confer implicit bias in online learning, contrasting with offline learning, and offers a new perspective on SGD's role.

Findings

Small batch sizes do not provide implicit bias benefits in online learning.

SGD noise mainly offers computational advantages in online regimes.

SGD in online learning acts as noisy steps along the noiseless gradient path.

Abstract

The success of SGD in deep learning has been ascribed by prior works to the implicit bias induced by finite batch sizes ("SGD noise"). While prior works focused on offline learning (i.e., multiple-epoch training), we study the impact of SGD noise on online (i.e., single epoch) learning. Through an extensive empirical analysis of image and language data, we demonstrate that small batch sizes do not confer any implicit bias advantages in online learning. In contrast to offline learning, the benefits of SGD noise in online learning are strictly computational, facilitating more cost-effective gradient steps. This suggests that SGD in the online regime can be construed as taking noisy steps along the "golden path" of the noiseless gradient descent algorithm. We study this hypothesis and provide supporting evidence in loss and function space. Our findings challenge the prevailing understanding of SGD and offer novel insights into its role in online learning.