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 to 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) convergence rate of FedAvg 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(t^2) where t is the index of communication rounds, but can stay 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 diversity combining - and further validating their performance advantages over the standard methods via extensive numerical experiments using several real-world FL tasks.

本研究旨在回答联邦学习在上下行通信均存在错误的情况下，可以处理多少通信噪声，以及对学习性能的影响。通过将上行和下行噪声通道明确地纳入联邦学习管道中，提出了几种新的联邦学习收敛性分析。结果表明，为了保持与无通信错误的理想情况相同的收敛行为，需要控制直接模型传输的上行和下行信噪比，使其随通信轮数的指数t的平方数量级增长，但可以在模型差分传输中保持不变。这些理论结果的关键洞察力是“低调飞行”原则 - 随机梯度下降是一种内在的嘈杂过程，只要上行/下行通信噪声不占支配地位，就可以容忍它们。

噪声通道上的联邦学习: 收敛分析和设计示例