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We consider a distributed learning problem in a wireless network, consistingof N distributed edge devices and a parameter server (PS). The objectivefunction is a sum of the edge devices' local loss functions, who aim to train ashared 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. Inthis paper, we develop a novel Accelerated Gradient-descent Multiple Access(AGMA) algorithm that uses momentum-based gradient signals over noisy fadingMAC to improve the convergence rate as compared to existing methods.Furthermore, AGMA does not require power control or beamforming to cancel thefading effect, which simplifies the implementation complexity. We analyze AGMAtheoretically, and establish a finite-sample bound of the error for both convexand strongly convex loss functions with Lipschitz gradient. For the stronglyconvex case, we show that AGMA approaches the best-known linear convergencerate as the network increases. For the convex case, we show that AGMAsignificantly improves the sub-linear convergence rate as compared to existingmethods. Finally, we present simulation results using real datasets thatdemonstrate better performance by AGMA.

Accelerated Gradient Descent Learning over Multiple Access Fading Channels