Riemannian SVRG with Barzilai-Borwein scheme for federated learning

Federated learning problems with non-convex constrains have many applications in practice. Based on the Riemannian federated SVRG (RFedSVRG), we proposed a modified RFedSVRG method by using the Barzilai-Borwein strategy (RFedSVRG-BB), which computed the step size automatically. We analyzed the convergence under the cases of geodesically strongly convex functions and non-convex functions, respectively. Numerical results for the principal component analysis problem, the federated kernel principal component analysis problem, and the Karcher mean problem on the positive defined cone was reported to demonstrate the effectiveness of the proposed Riemannian method.