Cost-Free Personalization via Information-Geometric Projection in Bayesian Federated Learning

TMLR Paper6369 Authors

Abstract: Bayesian Federated Learning (BFL) combines uncertainty modeling with decentralized training, enabling the development of personalized and reliable models in the presence of 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 the 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 in the statistical manifold, allowing us to derive closed-form solutions and achieve cost-free personalization. We apply the proposed approach within a variational learning setup using the Improved Variational Online Newton (IVON) optimizer and extend it 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.

Submission Type: Regular submission (no more than 12 pages of main content)

Assigned Action Editor: ~Feng_Zhou9

Submission Number: 6369