Weighted Over-the-Air Federated Learning

This paper introduces a new federated learning scheme that leverages over-the-air computation. The novel feature of this scheme is the proposal to employ adaptive weights during aggregation, as opposed to predefined weights in existing over-the-air schemes. This can mitigate the impact of wireless channel conditions on learning performance, without needing channel state information at transmitter side (CSIT). We derive convergence bound for the proposed scheme, supplemented with design insights. Accordingly, we propose an aggregation selection problem and develop an efficient algorithm to solve it, yielding optimized weights for the aggregation. Finally, through numerical experiments, we validate the effectiveness of the proposed scheme. Even with the challenges posed by channel conditions and device heterogeneity, the proposed scheme significantly surpasses other over-the-air schemes, including the one with CSIT.