Mirror Descent on Riemannian Manifolds
Researchers have developed a generalized framework for Mirror Descent (MD) on Riemannian manifolds, extending its applicability to complex optimization problems. This new Riemannian Mirror Descent (RMD) framework includes a stochastic variant and provides non-asymptotic convergence guarantees. The RMD framework simplifies to Curvilinear Gradient Descent (CGD) when applied to the Stiefel manifold, and its stochastic extension effectively tackles large-scale manifold optimization. AI