Technical Report: On the Convergence of Gossip Learning in the Presence of Node Inaccessibility

Gossip learning (GL), as a decentralized alternative to federated learning (FL), is more suitable for resource-constrained wireless networks, such as Flying Ad-Hoc Networks (FANETs) that are formed by unmanned aerial vehicles (UAVs). GL can significantly enhance the efficiency and extend the battery life of UAV networks. Despite the advantages, the performance of GL is strongly affected by data distribution, communication speed, and network connectivity. However, how these factors influence the GL convergence is still unclear. Existing work studied the convergence of GL based on a virtual quantity for the sake of convenience, which failed to reflect the real state of the network when some nodes are inaccessible. In this paper, we formulate and investigate the impact of inaccessible nodes to GL under a dynamic network topology. We first decompose the weight divergence by whether the node is accessible or not. Then, we investigate the GL convergence under the dynamic of node accessibility and theoretically provide how the number of inaccessible nodes, data non-i.i.d.-ness, and duration of inaccessibility affect the convergence. Extensive experiments are carried out in practical settings to comprehensively verify the correctness of our theoretical findings.