Decentralized federated learning (DFL) has gained popularity due to its practicality across various applications. Compared to the centralized version, training a shared model among a large number of nodes in DFL is more challenging, as there is no central server to coordinate the training process. Especially when distributed nodes suffer from limitations in communication or computational resources, DFL will experience extremely inefficient and unstable training. Motivated by these challenges, in this paper, we develop a novel algorithm based on the framework of the inexact alternating direction method (iADM). On one hand, our goal is to train a shared model with a sparsity constraint. This constraint enables us to leverage one-bit compressive sensing (1BCS), allowing transmission of one-bit information among neighbour nodes. On the other hand, communication between neighbour nodes occurs only at certain steps, reducing the number of communication rounds. Therefore, the algorithm exhibits notable communication efficiency. Additionally, as each node selects only a subset of neighbours to participate in the training, the algorithm is robust against stragglers. Additionally, complex items are computed only once for several consecutive steps and subproblems are solved inexactly using closed-form solutions, resulting in high computational efficiency. Finally, numerical experiments showcase the algorithm's effectiveness in both communication and computation.

翻译：去中心化联邦学习（DFL）因其在各类应用中的实用性而日益普及。与中心化版本相比，在DFL中训练大量节点间的共享模型更具挑战性，因为缺乏中央服务器来协调训练过程。尤其是当分布式节点面临通信或计算资源限制时，DFL将经历极其低效且不稳定的训练。受这些挑战启发，本文基于非精确交替方向法（iADM）框架提出了一种新型算法。一方面，我们的目标是在稀疏约束下训练共享模型。该约束使得我们能够利用单比特压缩感知（1BCS），从而在相邻节点间传输单比特信息。另一方面，相邻节点间的通信仅发生在特定步骤，减少了通信轮次。因此，该算法展现出显著的通信效率。此外，由于每个节点仅选择部分邻居参与训练，该算法对掉队节点具有鲁棒性。同时，复杂项在连续多个步骤中仅计算一次，且子问题通过闭式解进行非精确求解，从而实现了高计算效率。最后，数值实验验证了该算法在通信与计算两方面的有效性。