Federated Learning on Riemannian Manifolds
This addresses federated learning problems like PCA and kPCA for applications such as smartphone-based ML, but it is incremental as it adapts an existing method to a new constraint type.
The paper tackles federated learning with nonconvex constraints by proposing RFedSVRG for optimization over Riemannian manifolds, showing significant advantages over existing methods in numerical experiments.
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.