Absence of spurious solutions far from ground truth: A low-rank analysis with high-order losses

arXiv:2403.06056v1 Announce Type: cross
Abstract: Matrix sensing problems exhibit pervasive non-convexity, plaguing optimization with a proliferation of suboptimal spurious solutions. Avoiding convergence to these critical points poses a major challenge. This work provides new theoretical insights that help demystify the intricacies of the non-convex landscape. In this work, we prove that under certain conditions, critical points sufficiently distant from the ground truth matrix exhibit favorable geometry by being strict saddle points rather than troublesome local minima. Moreover, we introduce the …

abstract analysis arxiv challenge convergence cs.lg eess.sp insights landscape losses low major math.oc matrix optimization sensing solutions truth type work