The recently developed Distributed Block Proximal Method, for solving stochastic big-data convex optimization problems, is studied in this letter 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.

On the Linear Convergence Rate of the Distributed Block Proximal Method / Farina Francesco; Notarstefano Giuseppe. - In: IEEE CONTROL SYSTEMS LETTERS. - ISSN 2475-1456. - ELETTRONICO. - 4:3(2020), pp. 9013053.779-9013053.784. [10.1109/LCSYS.2020.2976311]

On the Linear Convergence Rate of the Distributed Block Proximal Method

Farina Francesco
;
Notarstefano Giuseppe
2020

Abstract

The recently developed Distributed Block Proximal Method, for solving stochastic big-data convex optimization problems, is studied in this letter 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.
2020
On the Linear Convergence Rate of the Distributed Block Proximal Method / Farina Francesco; Notarstefano Giuseppe. - In: IEEE CONTROL SYSTEMS LETTERS. - ISSN 2475-1456. - ELETTRONICO. - 4:3(2020), pp. 9013053.779-9013053.784. [10.1109/LCSYS.2020.2976311]
Farina Francesco; Notarstefano Giuseppe
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/806536
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