In this paper, a communication-efficient federated learning (FL) framework is proposed for improving the convergence rate of FL under a limited uplink capacity. The central idea of the proposed framework is to transmit the values and positions of the top-$S$ entries of a local model update for uplink transmission. A lossless encoding technique is considered for transmitting the positions of these entries, while a linear transformation followed by the Lloyd-Max scalar quantization is considered for transmitting their values. For an accurate reconstruction of the top-$S$ values, a linear minimum mean squared error method is developed based on the Bussgang decomposition. Moreover, an error feedback strategy is introduced to compensate for both compression and reconstruction errors. The convergence rate of the proposed framework is analyzed for a non-convex loss function with consideration of the compression and reconstruction errors. From the analytical result, the key parameters of the proposed framework are optimized for maximizing the convergence rate for the given capacity. Simulation results on the MNIST and CIFAR-10 datasets demonstrate that the proposed framework outperforms state-of-the-art FL frameworks in terms of classification accuracy under the limited uplink capacity.

翻译：本文针对上行容量受限场景，提出了一种通信高效的联邦学习框架以提升其收敛速率。该框架的核心思想是仅传输本地模型更新的前$S$个最大元素的值及其位置信息用于上行链路通信。在传输元素位置时采用无损编码技术，而传输元素值时则采用线性变换结合劳埃德-马克斯标量量化的方法。为实现对前$S$个值的精确重构，基于布桑分解开发了线性最小均方误差方法。此外引入误差反馈策略以补偿压缩与重构误差。本文考虑压缩与重构误差后，分析了该框架在非凸损失函数下的收敛速率。根据分析结果，针对给定容量条件优化了框架关键参数以最大化收敛速率。在MNIST与CIFAR-10数据集上的仿真结果表明，在上行容量受限情况下，本框架在分类精度上优于当前最优的联邦学习框架。