Bayesian AirComp with Sign-Alignment Precoding for Wireless Federated Learning

Abstract

This thesis considers the problem of wireless federated learning based on sign stochastic gradient descent (signSGD) algorithm via a multiple access channel. When sending locally computed gradient's sign information, each mobile device requires to apply precoding to circumvent wireless fading effects. In practice, however, acquiring perfect knowledge of channel state information (CSI) at all mobile devices is infeasible. This thesis presents a simple yet effective precoding method with limited channel knowledge, called sign-alignment precoding. The idea of sign-alignment precoding is to protect sign-flipping errors from wireless fadings. Under the Gaussian prior assumption on the local gradients, I also derives the mean squared error (MSE)-optimal aggregation function called Bayesian over-the-air computation (BayAirComp). The key finding of the thesis is that one-bit precoding with BayAirComp aggregation can provide a better learning performance than the existing precoding method even using perfect CSI with AirComp aggregation.