Distributed and Inexact Proximal Gradient Method for Online Convex Optimization

Fuente: arXiv
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Hauptverfasser: Bastianello, Nicola, Dall'Anese, Emiliano
Format: Preprint
Veröffentlicht: 2020
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author Bastianello, Nicola
Dall'Anese, Emiliano
author_facet Bastianello, Nicola
Dall'Anese, Emiliano
contents This paper develops and analyzes an online distributed proximal-gradient method (DPGM) for time-varying composite convex optimization problems. Each node of the network features a local cost that includes a smooth strongly convex function and a non-smooth convex function, both changing over time. By coordinating through a connected communication network, the nodes collaboratively track the trajectory of the minimizers without exchanging their local cost functions. The DPGM is implemented in an online fashion, that is, in a setting where only a limited number of steps are implemented before the function changes. Moreover, the algorithm is analyzed in an inexact scenario, that is, with a source of additive noise, that can represent e.g. communication noise or quantization. It is shown that the tracking error of the online inexact DPGM is upper-bounded by a convergent linear system, guaranteeing convergence within a neighborhood of the optimal solution.
format Preprint
id arxiv_https___arxiv_org_abs_2001_00870
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle Distributed and Inexact Proximal Gradient Method for Online Convex Optimization
Bastianello, Nicola
Dall'Anese, Emiliano
Optimization and Control
This paper develops and analyzes an online distributed proximal-gradient method (DPGM) for time-varying composite convex optimization problems. Each node of the network features a local cost that includes a smooth strongly convex function and a non-smooth convex function, both changing over time. By coordinating through a connected communication network, the nodes collaboratively track the trajectory of the minimizers without exchanging their local cost functions. The DPGM is implemented in an online fashion, that is, in a setting where only a limited number of steps are implemented before the function changes. Moreover, the algorithm is analyzed in an inexact scenario, that is, with a source of additive noise, that can represent e.g. communication noise or quantization. It is shown that the tracking error of the online inexact DPGM is upper-bounded by a convergent linear system, guaranteeing convergence within a neighborhood of the optimal solution.
title Distributed and Inexact Proximal Gradient Method for Online Convex Optimization
topic Optimization and Control
url https://arxiv.org/abs/2001.00870