D$^2$: Decentralized Training over Decentralized Data

TL;DR

This paper introduces D$^2$, a decentralized stochastic gradient descent algorithm that effectively handles large data variance across workers, improving convergence and robustness in decentralized machine learning settings.

Contribution

D$^2$ extends D-PSGD with variance reduction, making decentralized training more robust to data heterogeneity among workers.

Findings

D$^2$ outperforms D-PSGD in image classification tasks.

D$^2$ achieves faster convergence rates under high data variance.

Empirical results demonstrate robustness of D$^2$ to data heterogeneity.

Abstract

While training a machine learning model using multiple workers, each of which collects data from their own data sources, it would be most useful when the data collected from different workers can be {\em unique} and {\em different}. Ironically, recent analysis of decentralized parallel stochastic gradient descent (D-PSGD) relies on the assumption that the data hosted on different workers are {\em not too different}. In this paper, we ask the question: {\em Can we design a decentralized parallel stochastic gradient descent algorithm that is less sensitive to the data variance across workers?} In this paper, we present D$^2$, a novel decentralized parallel stochastic gradient descent algorithm designed for large data variance \xr{among workers} (imprecisely, "decentralized" data). The core of D$^2$ is a variance blackuction extension of the standard D-PSGD algorithm, which improves the convergence rate from $O\left({\sigma \over \sqrt{nT}} + {(n\zeta^2)^{\frac{1}{3}} \over T^{2/3}}\right)$ to $O\left({\sigma \over \sqrt{nT}}\right)$ where $\zeta^{2}$ denotes the variance among data on different workers. As a result, D$^2$ is robust to data variance among workers. We empirically evaluated D$^2$ on image classification tasks where each worker has access to only the data of a limited set of labels, and find that D$^2$ significantly outperforms D-PSGD.