Cost-Free Personalization via Information-Geometric Projection in Bayesian Federated Learning
This work addresses the problem of developing personalized and reliable models in federated learning for applications with data heterogeneity and privacy constraints, representing an incremental improvement over existing personalization mechanisms.
The paper tackles the challenge of personalizing Bayesian Federated Learning models under data heterogeneity by proposing an information-geometric projection framework that projects the global model onto a neighborhood of the user's local model, achieving a tunable trade-off between global generalization and local specialization with minimal computational overhead.
Bayesian Federated Learning (BFL) combines uncertainty modeling with decentralized training, enabling the development of personalized and reliable models under data heterogeneity and privacy constraints. Existing approaches typically rely on Markov Chain Monte Carlo (MCMC) sampling or variational inference, often incorporating personalization mechanisms to better adapt to local data distributions. In this work, we propose an information-geometric projection framework for personalization in parametric BFL. By projecting the global model onto a neighborhood of the user's local model, our method enables a tunable trade-off between global generalization and local specialization. Under mild assumptions, we show that this projection step is equivalent to computing a barycenter on the statistical manifold, allowing us to derive closed-form solutions and achieve cost-free personalization. We apply the proposed approach to a variational learning setup using the Improved Variational Online Newton (IVON) optimizer and extend its application to general aggregation schemes in BFL. Empirical evaluations under heterogeneous data distributions confirm that our method effectively balances global and local performance with minimal computational overhead.