The hierarchical collaborative learning within Low Earth Orbit (LEO) satellite constellations, termed LEO-HCL, is gaining increasing popularity by integrating intra-orbit Inter-Satellite Links and orbital edge computing to alleviate the latency issues caused by intermittent satellite connectivity in satellite-ground training architectures. However, LEO-HCL systems are confronted with a triad of challenges: the variable topology induced by satellite mobility, limited onboard computing and communication resources, and stringent energy constraints. In response to these challenges, we propose an energy-efficient training algorithm called FedAAC, which adaptively optimizes both aggregation frequency and model compression ratio within the resource-constrained LEO network. We have conducted a theoretical analysis of model convergence and investigated the relationship between convergence, aggregation frequency, and model compression ratio. Building on this analysis, we offer an approximation algorithm that dynamically calculates the optimal aggregation frequency and compression ratio during the training process. Extensive simulations have demonstrated that FedAAC significantly outperforms existing methods, offering enhanced convergence speed and energy efficiency. Compared to prior solutions, FedAAC achieves a 60% reduction in energy consumption, a 70% decrease in training time, and a 52% lower communication overhead.

Client-edge-cloud Federated Learning (CEC-FL) is emerging as an increasingly popular FL paradigm, alleviating the performance limitations of conventional cloud-centric Federated Learning (FL) by incorporating edge computing. However, improving training efficiency while retaining model convergence is not easy in CEC-FL. Although controlling aggregation frequency exhibits great promise in improving efficiency by reducing communication overhead, existing works still struggle to simultaneously achieve satisfactory training efficiency and model convergence performance in heterogeneous and dynamic environments. This paper proposes FedAda, a communication-efficient CEC-FL training method that aims to enhance training performance while ensuring model convergence through adaptive aggregation frequency adjustment. To this end, we theoretically analyze the model convergence under aggregation frequency control. Based on this analysis of the relationship between model convergence and aggregation frequencies, we propose an approximation algorithm to calculate aggregation frequencies, considering convergence and aligning with heterogeneous and dynamic node capabilities, ultimately achieving superior convergence accuracy and speed. Simulation results validate the effectiveness and efficiency of FedAda, demonstrating up to 4% improvement in test accuracy, 6.8× shorter training time and 3.3× less communication overhead compared to prior solutions.