Convergence of Distributed Stochastic Variance Reduced Methods Without Sampling Extra Data

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 reduce...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 68; pp. 3976 - 3989
Main Authors: Cen, Shicong, Zhang, Huishuai, Chi, Yuejie, Chen, Wei, Liu, Tie-Yan
Format: Journal Article
Language:English
Published: New York IEEE 2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Convergence
Distributed databases
Distributed optimization
Empirical analysis
Homogeneity
master/slave model
Optimization
Regularization
Risk management
Servers
Signal processing algorithms
Smoothness
stochastic optimization
Stochastic processes
variance reduction
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Summary: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. Furthermore, we show that when the data are less balanced, regularization can be used to ensure convergence at a slower rate. We also demonstrate that our analysis can be further extended to handle nonconvex loss functions.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2020.3005291