Inexact subgradient methods for semialgebraic functions

arXiv:2404.19517v1 Announce Type: cross
Abstract: Motivated by the widespread use of approximate derivatives in machine learning and optimization, we study inexact subgradient methods with non-vanishing additive errors and step sizes. In the nonconvex semialgebraic setting, under boundedness assumptions, we prove that the method provides points that eventually fluctuate close to the critical set at a distance proportional to $\epsilon^\rho$ where $\epsilon$ is the error in subgradient evaluation and $\rho$ relates to the geometry of the problem. In the convex setting, …

abstract arxiv assumptions derivatives errors eventually functions machine machine learning math.oc optimization prove set stat.ml study type