Comment on "First-order methods almost always avoid strict saddle points"

Abstract

The analysis on the global stability of Riemannian gradient descent method in manifold optimization (i.e., it avoids strict saddle points for almost all initializations) due to Lee et al. (Math. Program. 176:311-337) is corrected. Moreover, an explicit bound on the step-size is presented by the newly introduced retraction L-smooth property.