Stability and Generalization of the Decentralized Stochastic Gradient Descent

TL;DR

This paper introduces a new formulation of decentralized stochastic gradient descent and provides the first stability and generalization guarantees, revealing that decentralization can impair SGD stability.

Contribution

It offers a novel formulation and theoretical analysis of decentralized SGD, establishing stability and generalization bounds under mild assumptions.

Findings

Decentralization can deteriorate the stability of SGD.

Theoretical guarantees are established for decentralized SGD.

Empirical verification confirms the theoretical insights.

Abstract

The stability and generalization of stochastic gradient-based methods provide valuable insights into understanding the algorithmic performance of machine learning models. As the main workhorse for deep learning, stochastic gradient descent has received a considerable amount of studies. Nevertheless, the community paid little attention to its decentralized variants. In this paper, we provide a novel formulation of the decentralized stochastic gradient descent. Leveraging this formulation together with (non)convex optimization theory, we establish the first stability and generalization guarantees for the decentralized stochastic gradient descent. Our theoretical results are built on top of a few common and mild assumptions and reveal that the decentralization deteriorates the stability of SGD for the first time. We verify our theoretical findings by using a variety of decentralized settings and benchmark machine learning models.