Private Over-the-Air Federated Learning at Band-Limited Edge

We investigate over-the-air federated learning (OTA-FL) that exploits over-the-air computing (AirComp) to integrate communication and computation seamlessly for FL. Privacy presents a serious obstacle for OTA-FL, as it can be compromised by maliciously manipulating channel state information (CSI). Moreover, the limited band at edge hinders OTA-FL from training large-scale models. It remains open how to enable a multitude of devices with constrained resources and sensitive data to collaboratively train a global model at band-limited edge. To tackle this, we design a novel algorithm PROBE building upon a lightweight over-the-air gradients aggregation rule PB-O-GAR. Specifically, PB-O-GAR combines a random sparsification-like dimension reduction with Gaussian perturbation to provide rigorous privacy and band-adapted communication. It elaborately calibrates the transmission signal according to devices' perceived CSI for heterogeneous power constraints accommodation and CSI attack resilience. We show that by utilizing the common randomness, which deviates from the conventional FL, random sparsification-like dimension reduction can augment privacy in addition to the intrinsic privacy amplification effect of AirComp. We establish near-optimal convergence rates and explicit trade-offs among privacy, communication and utility for PROBE. Finally, extensive experiments on benchmark datasets are conducted to validate our theoretical findings and showcase the superiority of PROBE in realistic settings.