Decentralized Federated Learning via Dynamic Topologies and MIMO Over-the-Air Computation

Decentralized Federated Learning (DFL) enables edge devices to perform collaborative model training in a distributed, peer-to-peer fashion, demonstrating significant advantages. However, DFL deployment encounters a core challenge: existing approaches cannot simultaneously achieve perfect consensus and communication efficiency in dynamic network environments. To address these challenges, this paper introduces over-the-air computation (AirComp) to boost communication efficiency by leveraging the natural superposition property of analog signals in wireless multiple access channels and employing efficient consensus algorithms to facilitate agreement and improve convergence accuracy. Specifically, we design and implement a novel multiple-input multiple-output (MIMO) BASE-GRAPH based AirComp-DFL (BA-DFL) framework to investigate the MIMO multiple access channel problem in over-the-air DFL under dynamic topologies. We conduct convergence analysis, with results encompassing both dynamic and static topological scenarios, reflecting the influence of dynamic topologies parameters and communication errors on MIMO OA-DFL performance in device-to-device (D2D) networks. The result indicates that subgraph length in topologies and communication errors significantly impact learning performance. Based on this, we formulate a comprehensive joint optimization approach that integrates communication and learning parameters to enhance overall system performance by simultaneously optimizing transceiver beamformers and dynamic network topologies. Extensive numerical simulations demonstrate the characteristic behaviors of various network structures and verify the significant improvement in learning performance achieved by our proposed algorithms.