Stubbornness-Aware Peer-to-Peer Bayesian Federated Learning Over Graphs
Edge devices such as sensors, vehicles, and industrial controllers often need to learn a shared predictive model without pooling raw data or relying on a central server, even when local data quality varies widely across devices. This paper proposes a fully decentralized, peer-to-peer Bayesian federated learning method that explicitly regulates the relative influence of newly observed local data and neighbor information via an agent-specific stubbornness parameter. In each communication round, every device performs a stubbornness-weighted Bayesian-type local update using a fresh sample, exchanges the resulting intermediate belief with one-hop neighbors, and then fuses received beliefs through graph-weighted aggregation. To accommodate different training stages and heterogeneous data, we further introduce 1) time-varying schedule that gradually transitions from fast early adaptation to stable late-stage refinement, and 2) data-quality-aware rule that assigns agent-specific stubbornness using a simple similarity score. We provide a finite-time analysis that yields performance guarantees and clarifies how emphasizing higher-quality, lower-noise agents accelerates learning. Experiments on distributed linear regression and decentralized image classification demonstrate faster convergence than common decentralized baselines and improved robustness when some agents hold biased, scarce, or uninformative data.