This paper analyzes the impact of imperfect communication channels on decentralized federated learning (D-FL) and subsequently determines the optimal number of local aggregations per training round, adapting to the network topology and imperfect channels. We start by deriving the bias of locally aggregated D-FL models under imperfect channels from the ideal global models requiring perfect channels and aggregations. The bias reveals that excessive local aggregations can accumulate communication errors and degrade convergence. Another important aspect is that we analyze a convergence upper bound of D-FL based on the bias. By minimizing the bound, the optimal number of local aggregations is identified to balance a trade-off with accumulation of communication errors in the absence of knowledge of the channels. With this knowledge, the impact of communication errors can be alleviated, allowing the convergence upper bound to decrease throughout aggregations. Experiments validate our convergence analysis and also identify the optimal number of local aggregations on two widely considered image classification tasks. It is seen that D-FL, with an optimal number of local aggregations, can outperform its potential alternatives by over 10% in training accuracy.

翻译：本文分析了不完美通信信道对去中心化联邦学习（D-FL）的影响，并据此确定了每轮训练中适应网络拓扑与不完美信道的最优本地聚合次数。我们首先推导出在不完美信道下，本地聚合的D-FL模型相对于需要完美信道与聚合的理想全局模型所产生的偏差。该偏差表明，过多的本地聚合会累积通信误差并降低收敛性能。另一个重要方面是，我们基于该偏差推导了D-FL的收敛上界。通过最小化该上界，在未知信道信息的情况下，确定了最优本地聚合次数以平衡通信误差的累积。当掌握信道信息时，通信误差的影响可得到缓解，使得收敛上界在整个聚合过程中持续下降。实验验证了我们的收敛性分析，并在两个广泛应用的图像分类任务中确定了最优本地聚合次数。结果表明，采用最优本地聚合次数的D-FL，其训练准确率可比潜在替代方案高出10%以上。