Does Federated Learning (FL) work when both uplink and downlink communications have errors? How much communication noise can FL handle and what is its impact on the learning performance? This work is devoted to answering these practically important questions by explicitly incorporating both uplink and downlink noisy channels in the FL pipeline. We present several novel convergence analyses of FL over simultaneous uplink and downlink noisy communication channels, which encompass full and partial clients participation, direct model and model differential transmissions, and non-independent and identically distributed (IID) local datasets. These analyses characterize the sufficient conditions for FL over noisy channels to have the same convergence behavior as the ideal case of no communication error. More specifically, in order to maintain the O(1/T)\mathcal {O}({1}/{T}) convergence rate of FED AVG with perfect communications, the uplink and downlink signal-to-noise ratio (SNR) for direct model transmissions should be controlled such that they scale as O(t2)\mathcal {O}(t^{2}) where t{t} is the index of communication rounds, but can stay O(1)\mathcal {O}(1) (i.e., constant) for model differential transmissions. The key insight of these theoretical results is a “flying under the radar” principle – stochastic gradient descent (SGD) is an inherent noisy process and uplink/downlink communication noises can be tolerated as long as they do not dominate the time-varying SGD noise. We exemplify these theoretical findings with two widely adopted communication techniques – transmit power control and receive diversity combining – and further validate their performance advantages over the standard methods via numerical experiments using several real-world FL tasks.

中文翻译：

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噪声通道上的联邦学习：收敛分析和设计示例


当上下行通信都出现错误时，联邦学习（FL）是否有效？ FL 可以处理多少通信噪音？它对学习成绩有何影响？这项工作致力于通过在 FL 管道中明确合并上行链路和下行链路噪声信道来回答这些实际重要的问题。我们提出了几种新颖的 FL 在同步上行链路和下行链路噪声通信信道上的收敛分析，其中包括全部和部分客户端参与、直接模型和模型差分传输以及非独立同分布 (IID) 本地数据集。这些分析描述了噪声信道上的 FL 具有与无通信错误的理想情况相同的收敛行为的充分条件。更具体地说，为了在完美通信的情况下保持FED AVG的O(1/T)\mathcal {O}({1}/{T})收敛速度，上行链路和下行链路信噪比(SNR)对于直接模型传输，应控制为 O(t2)\mathcal {O}(t^{2})，其中 t{t} 是通信轮数的索引，但可以保持 O(1)\mathcal { O}(1)（即常数）用于模型差速传动。这些理论结果的关键见解是“雷达下飞行”原理 - 随机梯度下降 (SGD) 是一个固有的噪声过程，只要上行链路/下行链路通信噪声不主导时变 SGD 噪声，就可以容忍它们。我们用两种广泛采用的通信技术——发射功率控制和接收分集组合——来例证这些理论发现，并通过使用几个现实世界的 FL 任务的数值实验进一步验证它们相对于标准方法的性能优势。