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Convergence of Distributed Stochastic Variance Reduced Methods without Sampling Extra Data by Cen, Shicong; Zhang, Huishuai; Chi, Yuejie; Chen, Wei; Liu, Tie-Yan is a scholarly article available to read on EtoBox.

What is Convergence of Distributed Stochastic Variance Reduced Methods without Sampling Extra Data about?

Stochastic variance reduced methods have gained a lot of interest recently for empirical risk minimization due to its appealing run time complexity. When the data size is large and disjointly stored on different machines, it becomes imperative to distribute the implementation of such variance reduced methods. In this paper, we consider a general framework that directly distributes popular stochastic variance reduced methods in the master/slave model, by assigning outer loops to the parameter server, and inner loops to worker machines. This framework is natural and friendly to implement, but its theoretical convergence is not well understood. We obtain a comprehensive understanding of algorithmic convergence with respect to data homogeneity by measuring the smoothness of the discrepancy between the local and global loss functions. We establish the linear convergence of distributed versions of a family of stochastic variance reduced algorithms, including those using accelerated and recursive gradient updates, for minimizing strongly convex losses. Our theory captures how the convergence of distributed algorithms behaves as the number of machines and the size of local data vary. Furth

Author

Cen, Shicong; Zhang, Huishuai; Chi, Yuejie; Chen, Wei; Liu, Tie-Yan

Published

2019

Language

EN