  We consider a distributed learning problem in a wireless network, consisting
of N distributed edge devices and a parameter server (PS). The objective
function is a sum of the edge devices' local loss functions, who aim to train a
shared model by communicating with the PS over multiple access channels (MAC).
This problem has attracted a growing interest in distributed sensing systems,
and more recently in federated learning, known as over-the-air computation. In
this paper, we develop a novel Accelerated Gradient-descent Multiple Access
(AGMA) algorithm that uses momentum-based gradient signals over noisy fading
MAC to improve the convergence rate as compared to existing methods.
Furthermore, AGMA does not require power control or beamforming to cancel the
fading effect, which simplifies the implementation complexity. We analyze AGMA
theoretically, and establish a finite-sample bound of the error for both convex
and strongly convex loss functions with Lipschitz gradient. For the strongly
convex case, we show that AGMA approaches the best-known linear convergence
rate as the network increases. For the convex case, we show that AGMA
significantly improves the sub-linear convergence rate as compared to existing
methods. Finally, we present simulation results using real datasets that
demonstrate better performance by AGMA.
