Best Effort Voting Power Control for Byzantine-resilient Federated Learning Over the Air

Analog aggregation based federated learning over the air (FLOA) provides high communication efficiency and privacy provisioning in edge computing paradigm. When all edge devices (workers) simultaneously upload their local updates to the parameter server (PS) through the commonly shared time-frequency resources, the PS can only obtains the averaged update rather than the individual local ones. As a result, such a concurrent transmission and aggregation scheme reduces the latency and costs of communication but makes FLOA vulnerable to Byzantine attacks. For the design of Byzantine-resilient FLOA, this paper starts from analyzing the channel inversion (CI) power control mechanism that is widely used in existing FLOA literature. Our theoretical analysis indicates that although CI can achieve good learning performance in the non-attacking scenarios, it fails to work well with limited defensive capability to Byzantine attacks. Then, we propose a novel scheme called the best effort voting (BEV) power control policy, integrated with stochastic gradient descent (SGD). Our proposed BEV-SGD improves the robustness of FLOA to Byzantine attacks, by allowing all the workers to send their local updates at their maximum transmit power. Under the strongest-attacking circumstance, we derive the expected convergence rates of FLOA with CI and BEV, respectively. The comparison reveals that our BEV outperforms its counterpart with CI in terms of better convergence behavior, which is verified by experimental simulations.