Approximate Proximal-Gradient Methods

Anis Hamadouche; Yun Wu; Andrew Michael Wallace; João F. C. Mota

doi:10.1109/SSPD51364.2021.9541509

Approximate Proximal-Gradient Methods

Anis Hamadouche, Yun Wu, Andrew Michael Wallace, João F. C. Mota

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

1 Citation (Scopus)

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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)
Publisher	IEEE
Pages	95-100
Number of pages	6
ISBN (Electronic)	9781665433143
DOIs	https://doi.org/10.1109/SSPD51364.2021.9541509
Publication status	Published - 15 Sept 2021
Event	10th Sensor Signal Processing for Defence Conference 2021 - Edinburgh, United Kingdom Duration: 14 Sept 2021 → 15 Sept 2021

Conference

Conference	10th Sensor Signal Processing for Defence Conference 2021
Abbreviated title	SSPD 2021
Country/Territory	United Kingdom
City	Edinburgh
Period	14/09/21 → 15/09/21

Keywords

Approximate Algorithms.
Convex Optimization
Proximal Gradient

ASJC Scopus subject areas

Signal Processing
Safety, Risk, Reliability and Quality
Instrumentation

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10.1109/SSPD51364.2021.9541509

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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 Michael} and Mota, {Jo{\~a}o 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 2021, SSPD 2021 ; Conference date: 14-09-2021 Through 15-09-2021",

year = "2021",

month = sep,

day = "15",

doi = "10.1109/SSPD51364.2021.9541509",

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T1 - Approximate Proximal-Gradient Methods

AU - Hamadouche, Anis

AU - Wu, Yun

AU - Wallace, Andrew Michael

AU - Mota, João F. C.

PY - 2021/9/15

Y1 - 2021/9/15

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

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U2 - 10.1109/SSPD51364.2021.9541509

DO - 10.1109/SSPD51364.2021.9541509

M3 - Conference contribution

SP - 95

EP - 100

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

PB - IEEE

T2 - 10th Sensor Signal Processing for Defence Conference 2021

Y2 - 14 September 2021 through 15 September 2021

ER -

Approximate Proximal-Gradient Methods

Abstract

Conference

Keywords

ASJC Scopus subject areas

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