Approximate proximal-gradient methods

Anis Hamadouche; Yun Wu; Andrew M. Wallace; Joao F.C. Mota

doi:10.1109/SSPD51364.2021.9541509

Approximate proximal-gradient methods

Anis Hamadouche, Yun Wu, Andrew M. Wallace, Joao F.C. Mota

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Citation (Scopus)

55 Downloads (Pure)

Abstract

We study the convergence of the Proximal-Gradient algorithm for convex composite problems when both the gradient and the proximal mapping are computed approximately. This scenario occurs when the gradient is computationally expensive and the proximal operator is not available in closed form and may be computed only up to a certain fixed precision. We establish tight deterministic bounds and propose new probabilistic upper bounds on the suboptimality of the function values along the iterations under some statistical assumptions on the perturbed iterates. We use the Proximal-Gradient algorithm to solve randomly generated LASSO problems while varying the fixed-point machine representation and the proximal computation precision.

Original language	English
Title of host publication	2021 Sensor Signal Processing for Defence Conference (SSPD): Proceedings
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)	9781665433143
ISBN (Print)	9781665433150
DOIs	https://doi.org/10.1109/SSPD51364.2021.9541509
Publication status	Published - 23 Sept 2021
Externally published	Yes
Event	10th Sensor Signal Processing for Defence Conference, SSPD 2021 - Edinburgh, United Kingdom Duration: 14 Sept 2021 → 15 Sept 2021

Publication series

Name	Sensor Signal Processing for Defence Conference (SSPD): Proceedings

Conference

Conference	10th Sensor Signal Processing for Defence Conference, SSPD 2021
Country/Territory	United Kingdom
City	Edinburgh
Period	14/09/2021 → 15/09/2021

Bibliographical note

Funding Information:
Work supported by UK’s EPSRC (EP/T026111/1, EP/S000631/1), and the MOD University Defence Research Collaboration.

Publisher Copyright:
© 2021 IEEE.

Keywords

Approximate Algorithms.
Convex Optimization
Proximal Gradient

ASJC Scopus subject areas

Signal Processing
Safety, Risk, Reliability and Quality
Instrumentation

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Approximate proximal-gradient methods
Copyright 2021, IEEE. This work is made available online in accordance with the publisher’s policies. Please refer to any applicable terms of use of the publisher.
Accepted author manuscript, 398 KBLicence: Unspecified

Cite this

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title = "Approximate proximal-gradient methods",

abstract = "We study the convergence of the Proximal-Gradient algorithm for convex composite problems when both the gradient and the proximal mapping are computed approximately. This scenario occurs when the gradient is computationally expensive and the proximal operator is not available in closed form and may be computed only up to a certain fixed precision. We establish tight deterministic bounds and propose new probabilistic upper bounds on the suboptimality of the function values along the iterations under some statistical assumptions on the perturbed iterates. We use the Proximal-Gradient algorithm to solve randomly generated LASSO problems while varying the fixed-point machine representation and the proximal computation precision.",

keywords = "Approximate Algorithms., Convex Optimization, Proximal Gradient",

author = "Anis Hamadouche and Yun Wu and Wallace, \{Andrew M.\} and Mota, \{Joao F.C.\}",

note = "Funding Information: Work supported by UK{\textquoteright}s EPSRC (EP/T026111/1, EP/S000631/1), and the MOD University Defence Research Collaboration. Publisher Copyright: {\textcopyright} 2021 IEEE.; 10th Sensor Signal Processing for Defence Conference, SSPD 2021 ; Conference date: 14-09-2021 Through 15-09-2021",

year = "2021",

month = sep,

day = "23",

doi = "10.1109/SSPD51364.2021.9541509",

language = "English",

isbn = "9781665433150",

series = "Sensor Signal Processing for Defence Conference (SSPD): Proceedings",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

booktitle = "2021 Sensor Signal Processing for Defence Conference (SSPD): Proceedings",

address = "United States",

}

Hamadouche, A, Wu, Y, Wallace, AM & Mota, JFC 2021, Approximate proximal-gradient methods. in 2021 Sensor Signal Processing for Defence Conference (SSPD): Proceedings. Sensor Signal Processing for Defence Conference (SSPD): Proceedings, Institute of Electrical and Electronics Engineers Inc., 10th Sensor Signal Processing for Defence Conference, SSPD 2021, Edinburgh, United Kingdom, 14/09/2021. https://doi.org/10.1109/SSPD51364.2021.9541509

Approximate proximal-gradient methods. / Hamadouche, Anis; Wu, Yun; Wallace, Andrew M. et al.
2021 Sensor Signal Processing for Defence Conference (SSPD): Proceedings. Institute of Electrical and Electronics Engineers Inc., 2021. (Sensor Signal Processing for Defence Conference (SSPD): Proceedings).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Approximate proximal-gradient methods

AU - Hamadouche, Anis

AU - Wu, Yun

AU - Wallace, Andrew M.

AU - Mota, Joao F.C.

PY - 2021/9/23

Y1 - 2021/9/23

N2 - We study the convergence of the Proximal-Gradient algorithm for convex composite problems when both the gradient and the proximal mapping are computed approximately. This scenario occurs when the gradient is computationally expensive and the proximal operator is not available in closed form and may be computed only up to a certain fixed precision. We establish tight deterministic bounds and propose new probabilistic upper bounds on the suboptimality of the function values along the iterations under some statistical assumptions on the perturbed iterates. We use the Proximal-Gradient algorithm to solve randomly generated LASSO problems while varying the fixed-point machine representation and the proximal computation precision.

AB - We study the convergence of the Proximal-Gradient algorithm for convex composite problems when both the gradient and the proximal mapping are computed approximately. This scenario occurs when the gradient is computationally expensive and the proximal operator is not available in closed form and may be computed only up to a certain fixed precision. We establish tight deterministic bounds and propose new probabilistic upper bounds on the suboptimality of the function values along the iterations under some statistical assumptions on the perturbed iterates. We use the Proximal-Gradient algorithm to solve randomly generated LASSO problems while varying the fixed-point machine representation and the proximal computation precision.

KW - Approximate Algorithms.

KW - Convex Optimization

KW - Proximal Gradient

U2 - 10.1109/SSPD51364.2021.9541509

DO - 10.1109/SSPD51364.2021.9541509

M3 - Conference contribution

AN - SCOPUS:85116501561

SN - 9781665433150

T3 - Sensor Signal Processing for Defence Conference (SSPD): Proceedings

BT - 2021 Sensor Signal Processing for Defence Conference (SSPD): Proceedings

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 10th Sensor Signal Processing for Defence Conference, SSPD 2021

Y2 - 14 September 2021 through 15 September 2021

ER -

Approximate proximal-gradient methods

Abstract

Publication series

Conference

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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Cite this