Deploying federated learning (FL) over wireless networks with resource-constrained devices requires balancing between accuracy, energy efficiency, and precision. Prior art on FL often requires devices to train deep neural networks (DNNs) using a 32-bit precision level for data representation to improve accuracy. However, such algorithms are impractical for resource-constrained devices since DNNs could require execution of millions of operations. Thus, training DNNs with a high precision level incurs a high energy cost for FL. In this paper, a quantized FL framework, that represents data with a finite level of precision in both local training and uplink transmission, is proposed. Here, the finite level of precision is captured through the use of quantized neural networks (QNNs) that quantize weights and activations in fixed-precision format. In the considered FL model, each device trains its QNN and transmits a quantized training result to the base station. Energy models for the local training and the transmission with the quantization are rigorously derived. An energy minimization problem is formulated with respect to the level of precision while ensuring convergence. To solve the problem, we first analytically derive the FL convergence rate and use a line search method. Simulation results show that our FL framework can reduce energy consumption by up to 53% compared to a standard FL model. The results also shed light on the tradeoff between precision, energy, and accuracy in FL over wireless networks.

翻译：在资源受限设备上通过无线网络部署联邦学习需要在准确率、能效和精度之间取得平衡。现有联邦学习技术通常要求设备使用32位精度进行数据表示以训练深度神经网络，从而提高准确率。然而，此类算法对资源受限设备并不实用，因为深度神经网络需要执行数百万次运算。因此，使用高精度训练深度神经网络会给联邦学习带来高昂的能量成本。本文提出了一种量化联邦学习框架，该框架在本地训练和上行传输中均以有限精度表示数据。其中，有限精度通过使用量化神经网络实现，该网络将权重和激活函数量化为定点精度格式。在所考虑的联邦学习模型中，每个设备训练其量化神经网络，并将量化后的训练结果传输至基站。本文严格推导了本地训练和量化传输的能量模型，并在确保收敛性的前提下，建立了一个关于精度水平的能量最小化问题。为解决该问题，我们首先解析推导了联邦学习的收敛速度，并采用线性搜索方法。仿真结果表明，与标准联邦学习模型相比，我们的联邦学习框架可将能耗降低高达53%。结果还揭示了无线网络联邦学习中精度、能量与准确率之间的权衡关系。