Federated learning (FL) as a promising edge-learning framework can effectively address the latency and privacy issues by featuring distributed learning at the devices and model aggregation in the central server. In order to enable efficient wireless data aggregation, over-the-air computation (AirComp) has recently attracted great attention. However, fading of wireless channels can produce aggregate distortions in an AirComp-based FL scheme. In this paper, we propose a modified federated averaging (FedAvg) algorithm by introducing the local learning rates and present the convergence analysis. To combat the distortion, the local learning rate is optimized to adapt the fading channel, which is termed as dynamic learning rate (DLR). We begin our discussion by considering multiple-input-single-output (MISO) scenario, since the underlying optimization problem is convex and has a closed-form solution. Our studies are extended to a more general multiple-input-multiple-output (MIMO) case and an iterative method is derived. We also present the asymptotic analysis and give a near-optimal and closed-form receive beamforming solution when the number of antennas approaches infinity. Extensive simulation results demonstrate the effectiveness of the proposed DLR scheme in reducing the aggregate distortion and guaranteeing the testing accuracy on the MNIST and CIFAR10 datasets. In addition, the asymptotic analysis and the close-form solution are verified through numerical simulations.

中文翻译：

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利用空中计算的联邦学习的学习率优化

联合学习 (FL) 作为一种有前途的边缘学习框架，可以通过在设备上进行分布式学习和在中央服务器中进行模型聚合来有效解决延迟和隐私问题。为了实现高效的无线数据聚合，空中计算（AirComp）最近引起了极大的关注。然而，无线信道的衰落会在基于 AirComp 的 FL 方案中产生聚合失真。在本文中，我们通过引入局部学习率并提出收敛性分析，提出了一种改进的联邦平均（FedAvg）算法。为了对抗失真，局部学习率被优化以适应衰落信道，这被称为动态学习率（DLR）。我们通过考虑多输入单输出 (MISO) 场景开始我们的讨论，因为底层优化问题是凸的并且有一个封闭形式的解决方案。我们的研究扩展到更一般的多输入多输出 (MIMO) 情况，并推导出迭代方法。我们还介绍了渐近分析，并在天线数量接近无穷大时给出了接近最优和封闭形式的接收波束成形解决方案。大量的仿真结果证明了所提出的 DLR 方案在减少聚合失真和保证 MNIST 和 CIFAR10 数据集的测试精度方面的有效性。此外，通过数值模拟验证了渐近分析和闭式解。我们还介绍了渐近分析，并在天线数量接近无穷大时给出了接近最优和封闭形式的接收波束成形解决方案。大量的仿真结果证明了所提出的 DLR 方案在减少聚合失真和保证 MNIST 和 CIFAR10 数据集的测试精度方面的有效性。此外，通过数值模拟验证了渐近分析和闭式解。我们还介绍了渐近分析，并在天线数量接近无穷大时给出了接近最优和封闭形式的接收波束成形解决方案。大量的仿真结果证明了所提出的 DLR 方案在减少聚合失真和保证 MNIST 和 CIFAR10 数据集的测试精度方面的有效性。此外，通过数值模拟验证了渐近分析和闭式解。