论文标题
关于Riemannian流形的联合学习
Federated Learning on Riemannian Manifolds
论文作者
论文摘要
联邦学习（FL）发现了基于智能手机应用的机器学习应用程序中的许多重要应用。尽管已经对FL进行了许多算法，但据我们所知，尚未研究具有非凸约限制的FL算法。本文研究了Riemannian歧管的FL，该歧管发现了重要的应用，例如联合PCA和联邦KPCA。我们提出了一种riemannian联合SVRG（RFEDSVRG）方法，以解决对Riemannian歧管的联合优化。我们在不同情况下分析其收敛速率。进行数值实验以将RFEDSVRG与FedAvg和FedProx的Riemannian对应物进行比较。我们从数值实验中观察到RFEDSVRG的优势很重要。
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.
