Decentralized federated learning (DFL) is a powerful framework of distributed machine learning and decentralized stochastic gradient descent (SGD) is a driving engine for DFL. The performance of decentralized SGD is jointly influenced by communication-efficiency and convergence rate. In this paper, we propose a general decentralized federated learning framework to strike a balance between communication-efficiency and convergence performance. The proposed framework performs both multiple local updates and multiple inter-node communications periodically, unifying traditional decentralized SGD methods. We establish strong convergence guarantees for the proposed DFL algorithm without the assumption of convex objective function. The balance of communication and computation rounds is essential to optimize decentralized federated learning under constrained communication and computation resources. For further improving communication-efficiency of DFL, compressed communication is applied to DFL, named DFL with compressed communication (C-DFL). The proposed C-DFL exhibits linear convergence for strongly convex objectives. Experiment results based on MNIST and CIFAR-10 datasets illustrate the superiority of DFL over traditional decentralized SGD methods and show that C-DFL further enhances communication-efficiency.
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