  The growing number of wireless edge devices has magnified challenges
concerning energy, bandwidth, latency, and data heterogeneity. These challenges
have become bottlenecks for distributed learning. To address these issues, this
paper presents a novel approach that ensures energy efficiency for
distributionally robust federated learning (FL) with over air computation
(AirComp). In this context, to effectively balance robustness with energy
efficiency, we introduce a novel client selection method that integrates two
complementary insights: a deterministic one that is designed for energy
efficiency, and a probabilistic one designed for distributional robustness.
Simulation results underscore the efficacy of the proposed algorithm, revealing
its superior performance compared to baselines from both robustness and energy
efficiency perspectives, achieving more than 3-fold energy savings compared to
the considered baselines.
