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# Title: D$^2$: Decentralized Training over Decentralized Data

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.
 Subjects: Distributed, Parallel, and Cluster Computing (cs.DC); Learning (cs.LG); Machine Learning (stat.ML) Cite as: arXiv:1803.07068 [cs.DC] (or arXiv:1803.07068v1 [cs.DC] for this version)

## Submission history

From: Hanlin Tang [view email]
[v1] Mon, 19 Mar 2018 17:59:11 GMT (61kb,D)