Decentralized stochastic gradient descent (SGD) is a driving engine for decentralized federated learning (DFL). The performance of decentralized SGD is jointly influenced by inter-node communications and local updates. In this paper, we propose a general DFL framework, which implements both multiple local updates and multiple inter-node communications periodically, to strike a balance between communication efficiency and model consensus. It can provide a general decentralized SGD analytical framework. We establish strong convergence guarantees for the proposed DFL algorithm without the assumption of convex objectives. The convergence rate of DFL can be optimized to achieve the balance of communication and computing costs under constrained resources. For improving communication efficiency of DFL, compressed communication is further introduced to the proposed DFL as a new scheme, 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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