To efficiently exploit the massive amounts of raw data that are increasingly being generated in mobile edge networks, federated learning (FL) has emerged as a promising distributed learning technique. By collaboratively training a shared learning model on edge devices, raw data transmission and storage are replaced by the exchange of the local computed parameters/gradients in FL, which thus helps address latency and privacy issues. However, the number of resource blocks when using traditional orthogonal transmission strategies for FL linearly scales with the number of participating devices, which conflicts with the scarcity of communication resources. To tackle this issue, over-the-air computation (AirComp) has emerged recently which leverages the inherent superposition property of wireless channels to perform one-shot model aggregation. However, the aggregation accuracy in AirComp suffers from the unfavorable wireless propagation environment. In this paper, we consider the use of intelligent reflecting surfaces (IRSs) to mitigate this problem and improve FL performance with AirComp. Specifically, a performance-oriented design scheme that directly minimizes the optimality gap of the loss function is proposed to accelerate the convergence of AirComp-based FL. We first analyze the convergence behavior of the FL procedure with the absence of channel fading and noise. Based on the obtained optimality gap which characterizes the impact of channel fading and noise in different communication rounds on the ultimate performance of FL, we propose both online and offline approaches to tackle the resulting design problem. Simulation results demonstrate that such a performance-oriented design strategy can achieve higher test accuracy than the conventional isolated mean square error (MSE) minimization approach in FL.

翻译：为高效利用移动边缘网络中日益生成的海量原始数据，联邦学习（FL）作为一种有前景的分布式学习技术应运而生。通过边缘设备协同训练共享学习模型，FL以交换本地计算的参数/梯度替代原始数据的传输与存储，从而有助于解决延迟和隐私问题。然而，采用传统正交传输策略时FL所需的资源块数量与参与设备数量呈线性增长，这与通信资源的稀缺性相矛盾。为应对这一挑战，近期兴起的空中计算（AirComp）技术利用无线信道的固有叠加特性实现单轮模型聚合。然而，AirComp的聚合精度却受到不利无线传播环境的影响。本文考虑利用智能反射面（IRS）缓解该问题，并提升采用AirComp的FL性能。具体而言，提出一种面向性能的设计方案，通过直接最小化损失函数的最优性差距来加速基于AirComp的FL收敛。我们首先分析了无信道衰落与噪声干扰下FL过程的收敛行为。基于反映不同通信轮次中信道衰落与噪声对FL最终性能影响的最优性差距，分别提出在线与离线两种方法来解决相应的设计问题。仿真结果表明，相较于传统隔离均方误差（MSE）最小化方法，该面向性能的设计策略能在FL中实现更高的测试精度。