Bayesian AirComp with Sign-Alignment Precoding for Wireless Federated Learning

TL;DR

This paper introduces a sign-alignment precoding method for wireless federated learning that improves gradient aggregation accuracy under limited channel knowledge, outperforming existing methods even with perfect CSI.

Contribution

The paper proposes a novel sign-alignment precoding technique and derives a Bayesian aggregation method, enhancing wireless federated learning performance with limited channel information.

Findings

Sign-alignment precoding effectively mitigates fading effects.

BayAirComp achieves lower MSE in gradient aggregation.

One-bit precoding with BayAirComp outperforms existing methods.

Abstract

In this paper, we consider 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. In this paper, we present 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, we also derive the mean squared error (MSE)-optimal aggregation function called Bayesian over-the-air computation (BayAirComp). Our key finding 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.