Coordinate Descent Without Coordinates: Tangent Subspace Descent on Riemannian Manifolds
Coordinate Descent Without Coordinates: Tangent Subspace Descent on Riemannian Manifolds
We extend coordinate descent to manifold domains and provide convergence analyses for geodesically convex and nonconvex smooth objective functions. Our key insight is to draw an analogy between coordinate blocks in Euclidean space and tangent subspaces of a manifold. Hence, our method is called tangent subspace descent (TSD). The core …