Convergence Time Optimization for Decentralized Federated Learning With LEO Satellites via Number Control

Decentralized Federated Learning (DFL) is a federated learning framework without any central controllers. With the development of Low Earth Orbit (LEO) satellite constellations, LEO satellites can be used to train a machine learning model collaboratively through DFL. However, due to the energy limitations of the satellites, DFL with satellites has higher requirements on the latency. In this article, we investigate how to minimize the convergence time of DFL with satellites by designing the number of satellites in each orbit and the number of orbits. In addition to considering the total energy cost and the distance constraints in satellite communication, we also consider guaranteeing the DFL performance in the problem of minimizing the convergence time. However, obtaining closed-form solutions to this problem is difficult since the target is non-convex and the performance is hard to evaluate directly. To address these issues, we derive an upper bound on the convergence time and transform it into a quasi-convex function first. Then, we derive the convergence bound of DFL with respect to the number of satellites and orbits. Based on these two bounds, we reformulate the problem and obtain the closed-form expressions of the optimal number of satellites and orbits. Simulation results confirm the impact of these numbers on the convergence time and verify the effectiveness of the proposed scheme.