- Conference Paper
We develop a new Riemannian descent algorithm that relies on momentum to improve over existing first-order methods for geodesically convex optimization. In contrast, accelerated convergence rates proved in prior work have only been shown to hold for geodesically strongly-convex objective functions. We further extend our algorithm to geodesically weakly-quasi-convex objectives. Our proofs of convergence rely on a novel estimate sequence that illustrates the dependency of the convergence rate on the curvature of the manifold. We validate our theoretical results empirically on several optimization problems defined on the sphere and on the manifold of positive definite matrices. Show more
Book titleProceedings of the 24th International Conference on Artificial Intelligence and Statistics (AISTATS 2021)
Journal / seriesProceedings of Machine Learning Research
Pages / Article No.
Organisational unit09462 - Hofmann, Thomas / Hofmann, Thomas
MoreShow all metadata