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.

Farina Francesco, Notarstefano Giuseppe (2020). On the Linear Convergence Rate of the Distributed Block Proximal Method. IEEE CONTROL SYSTEMS LETTERS, 4(3), 779-784 [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
Farina Francesco, Notarstefano Giuseppe (2020). On the Linear Convergence Rate of the Distributed Block Proximal Method. IEEE CONTROL SYSTEMS LETTERS, 4(3), 779-784 [10.1109/LCSYS.2020.2976311].
Farina Francesco; Notarstefano Giuseppe
File in questo prodotto:
File Dimensione Formato  
main_L-CSS_final_disclaimer.pdf

accesso aperto

Tipo: Postprint
Licenza: Licenza per accesso libero gratuito
Dimensione 504.75 kB
Formato Adobe PDF
504.75 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/806536
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact