  Federated learning (FL) has found many important applications in
smart-phone-APP based machine learning applications. Although many algorithms
have been studied for FL, to the best of our knowledge, algorithms for FL with
nonconvex constraints have not been studied. This paper studies FL over
Riemannian manifolds, which finds important applications such as federated PCA
and federated kPCA. We propose a Riemannian federated SVRG (RFedSVRG) method to
solve federated optimization over Riemannian manifolds. We analyze its
convergence rate under different scenarios. Numerical experiments are conducted
to compare RFedSVRG with the Riemannian counterparts of FedAvg and FedProx. We
observed from the numerical experiments that the advantages of RFedSVRG are
significant.
