Adding vs. Averaging in Distributed Primal-Dual Optimization

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Chenxin Ma, Virginia Smith, Martin Jaggi, Michael Jordan, Peter Richtarik, Martin Takac ;
Proceedings of the 32nd International Conference on Machine Learning, PMLR 37:1973-1982, 2015.

Abstract

Distributed optimization methods for large-scale machine learning suffer from a communication bottleneck. It is difficult to reduce this bottleneck while still efficiently and accurately aggregating partial work from different machines. In this paper, we present a novel generalization of the recent communication-efficient primal-dual framework (COCOA) for distributed optimization. Our framework, COCOA+, allows for additive combination of local updates to the global parameters at each iteration, whereas previous schemes only allow conservative averaging. We give stronger (primal-dual) convergence rate guarantees for both COCOA as well as our new variants, and generalize the theory for both methods to cover non-smooth convex loss functions. We provide an extensive experimental comparison that shows the markedly improved performance of COCOA+ on several real-world distributed datasets, especially when scaling up the number of machines.

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