Decentralized federated learning (DFL) is a variant of federated learning, where edge nodes only communicate with their one-hop neighbors to learn the optimal model. However, as information exchange is restricted in a range of one-hop in DFL, inefficient information exchange leads to more communication rounds to reach the targeted training loss. This greatly reduces the communication efficiency. In this paper, we propose a new non-uniform quantization of model parameters to improve DFL convergence. Specifically, we apply the Lloyd-Max algorithm to DFL (LM-DFL) first to minimize the quantization distortion by adjusting the quantization levels adaptively. Convergence guarantee of LM-DFL is established without convex loss assumption. Based on LM-DFL, we then propose a new doubly-adaptive DFL, which jointly considers the ascending number of quantization levels to reduce the amount of communicated information in the training and adapts the quantization levels for non-uniform gradient distributions. Experiment results based on MNIST and CIFAR-10 datasets illustrate the superiority of LM-DFL with the optimal quantized distortion and show that doubly-adaptive DFL can greatly improve communication efficiency.

翻译：去中心化联邦学习是联邦学习的一种变体，其中边缘节点仅与其单跳邻居通信以学习最优模型。然而，由于去中心化联邦学习中信息交换局限于单跳范围，低效的信息交换导致达到目标训练损失需要更多通信轮次，这极大降低了通信效率。本文提出一种新的模型参数非均匀量化方法以改进去中心化联邦学习的收敛性。具体而言，我们首次将Lloyd-Max算法应用于去中心化联邦学习，通过自适应调整量化级别来最小化量化失真。在不假设损失函数为凸函数的情况下，建立了LM-DFL的收敛保证。基于LM-DFL，我们进一步提出一种新的双重自适应去中心化联邦学习，该方案联合考虑量化级别的递增数量以减少训练过程中的通信信息量，并针对非均匀梯度分布自适应调整量化级别。基于MNIST和CIFAR-10数据集的实验结果表明，具有最优量化失真的LM-DFL具有优越性，且双重自适应去中心化联邦学习能显著提升通信效率。