Finding an approximate second-order stationary point (SOSP) is a well-studied and fundamental problem in stochastic nonconvex optimization with many applications in machine learning.

Huber's contaminated heavy-tailed rewards and meanwhile needs to ensure differential privacy.

Huber's contaminated heavy-tailed rewards and meanwhile needs to ensure differential privacy.

Each participating individual should be able tocontribute without the fearofleaking one'ssensitiveinformation. At the same time, thesystem should berobustinthepresence ofmalicious participants inserting corrupted data. Recent algorithmic advances in learning from shared data focus on either one of these threats, leaving the system vulnerable to the other.

We consider a standard stability condition from the recent robust statistics literature and prove that, except with exponentially small failure probability, there exists a large fraction of the inliers satisfying this condition.

Finding an approximate second-order stationary point (SOSP) is a well-studied and fundamental problem in stochastic nonconvex optimization with many applications in machine learning.