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，由于在DFL中信息交换被限制在单跳范围内，低效的信息交换会导致达到目标训练损失所需的通信轮次增加，这极大地降低了通信效率。在本文中，我们提出了一种新的模型参数非均匀量化方法，以提升DFL的收敛性能。具体而言，我们首次将Lloyd-Max算法应用于DFL，通过自适应调整量化级别来最小化量化失真。在不假设凸损失函数的情况下，建立了LM-DFL的收敛保证。基于LM-DFL，我们进一步提出了一种新的双重自适应DFL方法，该方法联合考虑量化级别的递增数量，以减少训练中通信的信息量，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，并且双重自适应DFL能够显著提升通信效率。