Yan Sun, Li Shen, Dacheng Tao

Both centralized and decentralized approaches have shown excellent performance and great application value in federated learning (FL). However, current studies do not provide sufficient evidence to show which one performs better. Although from the optimization perspective, decentralized methods can approach the comparable convergence of centralized methods with less communication, its test performance has always been inefficient in empirical studies. To comprehensively explore their behaviors in FL, we study their excess risks, including the joint analysis of both optimization and generalization. We prove that on smooth non-convex objectives, 1) centralized FL (CFL) always generalizes better than decentralized FL (DFL); 2) from perspectives of the excess risk and test error in CFL, adopting partial participation is superior to full participation; and, 3) there is a necessary requirement for the topology in DFL to avoid performance collapse as the training scale increases. Based on some simple hardware metrics, we could evaluate which framework is better in practice. Extensive experiments are conducted on common setups in FL to validate that our theoretical analysis is contextually valid in practical scenarios.