Robust Second-Order Nonconvex Optimization and Its Application to Low Rank Matrix Sensing

arXiv:2403.10547v1 Announce Type: cross
Abstract: 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. However, this problem is poorly understood in the presence of outliers, limiting the use of existing nonconvex algorithms in adversarial settings.
In this paper, we study the problem of finding SOSPs in the strong contamination model, where a constant fraction of datapoints are arbitrarily corrupted. We introduce a general framework for efficiently …

abstract adversarial algorithms application applications arxiv cs.ai cs.ds cs.lg however low machine machine learning math.oc matrix optimization outliers robust sensing stochastic type