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.

本研究分析了不完美通信渠道对分散式联邦学习（D-FL）的影响，并确定了每轮训练的最佳本地汇总次数，以适应网络拓扑和不完美通道。通过从需要完美通道和汇总的理想全局模型中推导出具有不完美通道的本地汇总D-FL模型的偏差，揭示了过多的本地汇总可能会积累通信错误并降低收敛性。本文还分析了基于该偏差的D-FL的收敛上限。通过最小化该上限，确定了在通道知识缺失的情况下平衡通信错误积累的最佳本地汇总次数。实验证实了我们的收敛分析，同时在两个广泛考虑的图像分类任务中确定了最佳的本地汇总次数。结果表明，在训练准确性方面，具有最佳本地汇总次数的D-FL可以比其潜在替代方案提高10%以上。

不完善通信信道上的分散式联邦学习