On the convergence result of the gradient-push algorithm on directed graphs with constant stepsize

02/17/2023

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by   Woocheol Choi, et al.

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Gradient-push algorithm has been widely used for decentralized optimization problems when the connectivity network is a direct graph. This paper shows that the gradient-push algorithm with stepsize α>0 converges exponentially fast to an O(α)-neighborhood of the optimizer under the assumption that each cost is smooth and the total cost is strongly convex. Numerical experiments are provided to support the theoretical convergence results.