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On the Linear Convergence Rate of the Distributed Block Proximal Method by Farina, Francesco; Notarstefano, Giuseppe is a scholarly article available to read on EtoBox.

What is On the Linear Convergence Rate of the Distributed Block Proximal Method about?

The recently developed Distributed Block Proximal Method, for solving stochastic big-data convex optimization problems, is studied in this paper under the assumption of constant stepsizes and strongly convex (possibly non-smooth) local objective functions. This class of problems arises in many learning and classification problems in which, for example, strongly-convex regularizing functions are included in the objective function, the decision variable is extremely high dimensional, and large datasets are employed. The algorithm produces local estimates by means of block-wise updates and communication among the agents. The expected distance from the (global) optimum, in terms of cost value, is shown to decay linearly to a constant value which is proportional to the selected local stepsizes. A numerical example involving a classification problem corroborates the theoretical results.

Author

Farina, Francesco; Notarstefano, Giuseppe

Published

2020

Language

EN