On the Linear Convergence Rate of the Distributed Block Proximal Method
Abstract
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.
Cite
@article{arxiv.2003.02659,
title = {On the Linear Convergence Rate of the Distributed Block Proximal Method},
author = {Francesco Farina and Giuseppe Notarstefano},
journal= {arXiv preprint arXiv:2003.02659},
year = {2020}
}
Comments
arXiv admin note: text overlap with arXiv:1905.04214