Min-Max Grassmannian Optimization for Online Subspace Tracking

Abstract

We propose GeRoST (Geometrically Robust Subspace Tracking), an online subspace tracking algorithm that models uncertainty in a subspace using a Grassmannian ball. We derive an exact scalar dual for the worst-case subspace problem, establish conditions for a unique worst-case subspace and a Riemannian gradient, and characterize the minimum radius needed to cover a dimensional extension of the target subspace. Each update uses either a spectral direction computed in a reduced subspace or the gradient of the window reconstruction loss. Our numerical experiments show that GeRoST achieves lower mean post-fault prediction error than GREAT in system identification. In video separation, it achieves higher precision and a better precision--recall balance, as measured by the F${}_1$ score, than both GREAT and GRASTA at the reported thresholds, with lower recall and longer runtime.

arXiv commentAccepted for the 65th IEEE Conference on Decision and Control, December 15-18 2026, Honolulu, Hawaii, USA