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Personalized Bayesian Federated Learning with Wasserstein Barycenter Aggregation
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Proposes FedWBA, a personalized Bayesian federated learning method that uses particle-based SVGD for client posteriors and Wasserstein barycenter aggregation of particles on the server, with local ELBO and global consistency guarantees.
Problem
Personalized Bayesian federated learning suffers from restrictive parametric (e.g., Gaussian) client posterior approximations and naive parameter averaging when aggregating posteriors on the server, which ignores the geometry of distributions.
Approach
Replace parametric variational posteriors with SVGD particles on clients and replace parameter averaging with a Wasserstein barycenter over particle sets on the server, computed in closed form via optimal transport plans; the global prior is then reconstructed with KDE for client-side SVGD.
Key results
- On MNIST with 50 clients, FedWBA reaches 97.99% accuracy vs 97.90% for pFedVEM (second best).
- On CIFAR-100 with 50 clients, FedWBA reaches 63.30%... reported as 64.21% vs 63.30% for pFedGP (second best).
- ECE on MNIST, FMNIST, CIFAR-10 with 50 clients: FedWBA 0.0014, 0.0078, 0.0132, lowest among compared methods.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use FedWBA rather than pFedVEM | MNIST, 50 clients · MNIST, 50 clients | accuracy (%): 97.90 -> 97.99 | No clear effect |
| use FedWBA rather than pFedGP | MNIST, 200 clients · MNIST, 200 clients | accuracy (%): 96.48 -> 96.95 | Helped |
| use FedWBA rather than DSVGD | FMNIST, 50 clients · FMNIST, 50 clients | accuracy (%): 92.41 -> 92.50 | No clear effect |
| use FedWBA rather than FedPer | CIFAR-10, 50 clients · CIFAR-10, 50 clients | accuracy (%): 73.53 -> 73.40 | No clear effect |
| use FedWBA rather than pFedVEM | CIFAR-10, 200 clients · CIFAR-10, 200 clients | accuracy (%): 70.10 -> 69.83 | Hurt |
| use FedWBA rather than pFedGP | CIFAR-100, 200 clients · CIFAR-100, 200 clients | accuracy (%): 59.10 -> 59.22 | No clear effect |
| use FedWBA rather than FedPer | FedWBA · MNIST, FMNIST, CIFAR-10, 50 clients | ECE: 0.0061 -> 0.0014; 0.0082 -> 0.0078; 0.0284 -> 0.0132 | Helped |
| increase SVGD iterations from 20 to 30 (ablation) | FedWBA on MNIST · MNIST, 100 clients | accuracy (%): 96.59 -> 97.02 | Helped |
| replace RBF with sigmoid SVGD kernel (ablation) | FedWBA · MNIST, 100 clients | accuracy (%): 97.23 -> 93.90 | Hurt |
| replace RBF with sigmoid SVGD kernel (ablation) | FedWBA · FMNIST, 100 clients | accuracy (%): 91.65 -> 87.10 | Hurt |
| set SVGD bandwidth to 1 rather than median heuristic (ablation) | FedWBA on MNIST · MNIST, 100 clients | accuracy (%): 97.26 -> 97.34 | Helped |
| set SVGD bandwidth to 12 rather than median heuristic (ablation) | FedWBA on MNIST · MNIST, 100 clients | accuracy (%): 97.26 -> 97.10 | Hurt |
Surprising findings
- The global model of FedWBA is slightly worse than FedAvg/Scaffold on MNIST with 200 clients (89.90% vs 90.85-90.94%), which the authors attribute to using it only as a prior regularizer.
Limitations
- Theoretical guarantees rely on strong assumptions (compactness, entropy bounds, metric property) and an ELBO bound that drops higher-order terms for small step sizes.
- DSVGD could not finish within 10 hours on CIFAR-10/CIFAR-100, so comparisons on those datasets are incomplete.
- Only 10 particles are used, limiting the nonparametric representation capacity.
Experimental setup
Datasets: MNIST FashionMNIST CIFAR-10 CIFAR-100
Benchmarks: MNIST FashionMNIST CIFAR-10 CIFAR-100
Metrics: test accuracy expected calibration error convergence rate
Baselines: FedAvg FedProx Scaffold FedPer PerFedAvg pFedME pFedBayes pFedVEM pFedGP DSVGD
Builds on: Stein variational gradient descent pFedBayes pFedVEM distributed SVGD pFedGP
Closest papers by meaning
- Harnessing Heterogeneous Statistical Strength for Personalized Federated Learning via Hierarchical Bayesian Inference (ICML 2025 · similarity 0.90)
- A Bayesian Approach for Personalized Federated Learning in Heterogeneous Settings (NeurIPS 2024 · similarity 0.88)
- Federated Generalised Variational Inference: A Robust Probabilistic Federated Learning Framework (ICML 2025 · similarity 0.88)
- Calibrated One Round Federated Learning with Bayesian Inference in the Predictive Space (AAAI 2024 · similarity 0.88)
- Improving Generalization in Federated Learning with Model-Data Mutual Information Regularization: A Posterior Inference Approach (NeurIPS 2024 · similarity 0.87)
- FedBEns: One-Shot Federated Learning based on Bayesian Ensemble (ICML 2025 · similarity 0.87)
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