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arXiv · 2008.06082

Push-SAGA: A decentralized stochastic algorithm with variance reduction over directed graphs

Muhammad I. Qureshi·Ran Xin·Soummya Kar·Usman A. Khan
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Abstract

In this paper, we propose Push-SAGA, a decentralized stochastic first-order method for finite-sum minimization over a directed network of nodes. Push-SAGA combines node-level variance reduction to remove the uncertainty caused by stochastic gradients, network-level gradient tracking to address the distributed nature of the data, and push-sum consensus to tackle the challenge of directed communication links. We show that Push-SAGA achieves linear convergence to the exact solution for smooth and strongly convex problems and is thus the first linearly-convergent stochastic algorithm over arbitrary strongly connected directed graphs. We also characterize the regimes in which Push-SAGA achieves a linear speed-up compared to its centralized counterpart and achieves a network-independent convergence rate. We illustrate the behavior and convergence properties of Push-SAGA with the help of numerical experiments on strongly convex and non-convex problems.

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BibTeXRIS

Muhammad I. Qureshi, Ran Xin, Soummya Kar, Usman A. Khan. 2020-08-13. Push-SAGA: A decentralized stochastic algorithm with variance reduction over directed graphs. https://arxiv.org/abs/2008.06082

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