BA-BFL: Barycentric Aggregation for Bayesian Federated Learning

In this work, we study the problem of aggregation in the context of Bayesian Federated Learning (BFL). Using an information geometric perspective, we interpret the BFL aggregation step as finding the barycenter of the trained posteriors for a pre-specified divergence metric. We study the barycenter problem for the parametric family of $\alpha$-divergences and, focusing on the standard case of independent and Gaussian distributed parameters, we recover the closed-form solution of the reverse Kullback-Leibler barycenter and develop the analytical form of the squared Wasserstein-2 barycenter. Considering a non-IID setup, where clients possess heterogeneous data, we analyze the performance of the developed algorithms against state-of-the-art (SOTA) Bayesian aggregation methods in terms of accuracy, uncertainty quantification (UQ), model calibration (MC), and fairness. Finally, we extend our analysis to the framework of Hybrid Bayesian Deep Learning (HBDL), where we study how the number of Bayesian layers in the architecture impacts the considered performance metrics. Our experimental results show that the proposed methodology presents comparable performance with the SOTA while offering a geometric interpretation of the aggregation phase.