How to Coordinate Edge Devices for Over-the-Air Federated Learning?

TL;DR

This paper investigates device coordination strategies for over-the-air federated learning in wireless networks, proposing a low-complexity algorithm that approximates optimal schemes and improves aggregation error management.

Contribution

It introduces a novel analytical framework and a low-complexity algorithm for device coordination in OTA-FL, addressing the NP-hard subset selection problem.

Findings

The proposed algorithm closely approximates the optimal scheme.

Optimal coordination schemes can be characterized by monotonic properties.

The method effectively reduces computational complexity in OTA-FL device selection.

Abstract

This work studies the task of device coordination in wireless networks for over-the-air federated learning (OTA-FL). For conventional metrics of aggregation error, the task is shown to describe the zero-forcing (ZF) and minimum mean squared error (MMSE) schemes and reduces to the NP-hard problem of subset selection. We tackle this problem by studying properties of the optimal scheme. Our analytical results reveal that this scheme is found by searching among the leaves of a tree with favorable monotonic features. Invoking these features, we develop a low-complexity algorithm that approximates the optimal scheme by tracking a dominant path of the tree sequentially. Our numerical investigations show that the proposed algorithm closely tracks the optimal scheme.