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A Projection-free Decentralized Algorithm for Non-convex Optimization

Abstract: 

This paper considers a decentralized projection free algorithm for non-convex optimization in high dimension. More specifically, we propose a Decentralized Frank-Wolfe (DeFW)
algorithm which is suitable when high dimensional optimization constraints are difficult to handle by conventional projection/proximal-based gradient descent methods. We present conditions under which the DeFW algorithm converges to a stationary point and prove that the rate of convergence is as fast as ${\cal O}( 1/\sqrt{T} )$, where
$T$ is the iteration number. This paper provides the first convergence guarantee for Frank-Wolfe methods applied to non-convex decentralized optimization. Utilizing our theoretical findings, we formulate a novel robust matrix completion problem and apply DeFW to give an efficient decentralized solution. Numerical experiments are performed on realistic and synthetic data to support our findings.

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Paper Details

Authors:
Anna Scaglione, Jean Lafond, Eric Moulines
Submitted On:
7 December 2016 - 11:58pm
Short Link:
Type:
Presentation Slides
Event:
Presenter's Name:
Hoi To Wai
Paper Code:
RMN-1.1
Document Year:
2016
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Document Files

ncvx_globalsip16.pdf

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[1] Anna Scaglione, Jean Lafond, Eric Moulines, "A Projection-free Decentralized Algorithm for Non-convex Optimization", IEEE SigPort, 2016. [Online]. Available: http://sigport.org/1381. Accessed: Sep. 26, 2020.
@article{1381-16,
url = {http://sigport.org/1381},
author = {Anna Scaglione; Jean Lafond; Eric Moulines },
publisher = {IEEE SigPort},
title = {A Projection-free Decentralized Algorithm for Non-convex Optimization},
year = {2016} }
TY - EJOUR
T1 - A Projection-free Decentralized Algorithm for Non-convex Optimization
AU - Anna Scaglione; Jean Lafond; Eric Moulines
PY - 2016
PB - IEEE SigPort
UR - http://sigport.org/1381
ER -
Anna Scaglione, Jean Lafond, Eric Moulines. (2016). A Projection-free Decentralized Algorithm for Non-convex Optimization. IEEE SigPort. http://sigport.org/1381
Anna Scaglione, Jean Lafond, Eric Moulines, 2016. A Projection-free Decentralized Algorithm for Non-convex Optimization. Available at: http://sigport.org/1381.
Anna Scaglione, Jean Lafond, Eric Moulines. (2016). "A Projection-free Decentralized Algorithm for Non-convex Optimization." Web.
1. Anna Scaglione, Jean Lafond, Eric Moulines. A Projection-free Decentralized Algorithm for Non-convex Optimization [Internet]. IEEE SigPort; 2016. Available from : http://sigport.org/1381