Cedric Josz — accepted AI-conference papers

2018

A theory on the absence of spurious solutions for nonconvex and nonsmooth optimization

Cedric Josz, Yi Ouyang, Richard Zhang, Javad Lavaei, Somayeh Sojoudi

NeurIPS 2018poster

We study the set of continuous functions that admit no spurious local optima (i.e. local minima that are not global minima) which we term global functions. They satisfy various powerful properties for analyzing nonconvex and nonsmooth optimization problems. For instance, they satisfy a theorem akin…

Cited by 54 Source ↗PDF ↗Scholar ↗

2018

How Much Restricted Isometry is Needed In Nonconvex Matrix Recovery?

Richard Zhang, Cedric Josz, Somayeh Sojoudi, Javad Lavaei

NeurIPS 2018spotlight

When the linear measurements of an instance of low-rank matrix recovery satisfy a restricted isometry property (RIP) --- i.e. they are approximately norm-preserving --- the problem is known to contain no spurious local minima, so exact recovery is guaranteed. In this paper, we show that moderate RIP…

Cited by 51 Source ↗PDF ↗Scholar ↗