We consider a many-to-one wireless architecture for federated learning at the network edge, where multiple edge devices collaboratively train a model using local data. The unreliable nature of wireless connectivity, together with constraints in computing resources at edge devices, dictates that the local updates at edge devices should be carefully crafted and compressed to match the wireless communication resources available and should work in concert with the receiver. Thus motivated, we propose SGD-based bandlimited coordinate descent algorithms for such settings. Specifically, for the wireless edge employing over-the-air computing, a common subset of k-coordinates of the gradient updates across edge devices are selected by the receiver in each iteration, and then transmitted simultaneously over k sub-carriers, each experiencing time-varying channel conditions. We characterize the impact of communication error and compression, in terms of the resulting gradient bias and mean squared error, on the convergence of the proposed algorithms. We then study learning-driven communication error minimization via joint optimization of power allocation and learning rates. Our findings reveal that optimal power allocation across different sub-carriers should take into account both the gradient values and channel conditions, thus generalizing the widely used water-filling policy. We also develop sub-optimal distributed solutions amenable to implementation.

本研究考虑了一种基于无线边缘网络的多对一联合学习架构，并提出了基于 SGD 的带限制坐标下降算法以适应无线通信资源。研究者还通过联合优化功率分配和学习速率以减少通信误差，并发现跨不同子载波的最佳功率分配应同时考虑梯度值和信道条件。最后，他们提出了一些可行的分布式解决方案来对该问题进行优化。

无线网络联合学习: 有限带宽协调下降方法