$D^2$: Decentralized Training over Decentralized Data

Hanlin Tang, Xiangru Lian, Ming Yan, Ce Zhang, Ji Liu
Proceedings of the 35th International Conference on Machine Learning, PMLR 80:4848-4856, 2018.

Abstract

While training a machine learning model using multiple workers, each of which collects data from its own data source, it would be useful when the data collected from different workers are unique and different. Ironically, recent analysis of decentralized parallel stochastic gradient descent (D-PSGD) relies on the assumption that the data hosted on different workers are not too different. In this paper, we ask the question: 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 reduction extension of D-PSGD. It 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v80-tang18a, title = {$D^2$: Decentralized Training over Decentralized Data}, author = {Tang, Hanlin and Lian, Xiangru and Yan, Ming and Zhang, Ce and Liu, Ji}, booktitle = {Proceedings of the 35th International Conference on Machine Learning}, pages = {4848--4856}, year = {2018}, editor = {Dy, Jennifer and Krause, Andreas}, volume = {80}, series = {Proceedings of Machine Learning Research}, month = {10--15 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v80/tang18a/tang18a.pdf}, url = {https://proceedings.mlr.press/v80/tang18a.html}, abstract = {While training a machine learning model using multiple workers, each of which collects data from its own data source, it would be useful when the data collected from different workers are unique and different. Ironically, recent analysis of decentralized parallel stochastic gradient descent (D-PSGD) relies on the assumption that the data hosted on different workers are not too different. In this paper, we ask the question: 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 reduction extension of D-PSGD. It 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.} }
Endnote
%0 Conference Paper %T $D^2$: Decentralized Training over Decentralized Data %A Hanlin Tang %A Xiangru Lian %A Ming Yan %A Ce Zhang %A Ji Liu %B Proceedings of the 35th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2018 %E Jennifer Dy %E Andreas Krause %F pmlr-v80-tang18a %I PMLR %P 4848--4856 %U https://proceedings.mlr.press/v80/tang18a.html %V 80 %X While training a machine learning model using multiple workers, each of which collects data from its own data source, it would be useful when the data collected from different workers are unique and different. Ironically, recent analysis of decentralized parallel stochastic gradient descent (D-PSGD) relies on the assumption that the data hosted on different workers are not too different. In this paper, we ask the question: 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 reduction extension of D-PSGD. It 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.
APA
Tang, H., Lian, X., Yan, M., Zhang, C. & Liu, J.. (2018). $D^2$: Decentralized Training over Decentralized Data. Proceedings of the 35th International Conference on Machine Learning, in Proceedings of Machine Learning Research 80:4848-4856 Available from https://proceedings.mlr.press/v80/tang18a.html.

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