Device Scheduling in Over-the-Air Federated Learning Via Matching Pursuit

Abstract

This paper develops a class of low-complexity device scheduling algorithms for over-the-air federated learning via the method of matching pursuit. The proposed scheme tracks closely the close-to-optimal performance achieved by difference-of-convex programming, and outperforms significantly the well-known benchmark algorithms based on convex relaxation. Compared to the state-of-the-art, the proposed scheme imposes a drastically lower computational load on the system: for $K$ devices and $N$ antennas at the parameter server, the benchmark complexity scales with $(N^{2}+K)^{3} + N^{6}$ while the complexity of the proposed scheme scales with ${K^{p} N^{q}}$ for some $0 \lt p,q \leq 2$ . The efficiency of the proposed scheme is confirmed through the convergence analysis and numerical experiments on CIFAR-10 dataset.