# A Projection-free Decentralized Algorithm for Non-convex Optimization

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Citation Author(s):
Anna Scaglione, Jean Lafond, Eric Moulines
Submitted by:
Hoi To Wai
Last updated:
7 December 2016 - 11:58pm
Document Type:
Presentation Slides
Document Year:
2016
Event:
Presenters Name:
Hoi To Wai
Paper Code:
RMN-1.1
Categories:

#### Abstract

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.

## ncvx_globalsip16.pdf

#### Dataset Files

ncvx_globalsip16.pdf

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