Arvin Tashakori pfedbl: Federated bayesian learning with personalized prior

Xinhui Yu, Arvin Tashakori, Liang Zou, Z. Jane Wang

Abstract: Most existing federated learning (FL) frameworks use deterministic models as the task model, which may suffer from overfitting due to small-scale data at client sides. Since Bayesian learning (BL) can quantify the uncertainty associated with both model parameters and prediction outcomes, there have been efforts to integrate BL with FL and the global objective is transformed into posterior approximation using Bayesian optimization. Variational inference is commonly used in such efforts which utilize the global distribution as the prior for the optimization of local Bayesian neural networks (BNNs) and thus eliminates the need for assigning specific prior distributions for clients. However, due to statistical heterogeneity across clients, the global distribution, representing the collective knowledge of all clients, may not be precise as client prior. To address this concern, we propose a federated Bayesian learning framework with personalized priors (pFedBL) where each client is assigned with a local BNN. Specifically, we first introduce a KL-divergence-based distribution aggregation scheme to ensure the effectiveness of the global distribution. Meanwhile, under the mild assumption that the server has access to a general unlabeled dataset, the server uses predictions as well as predictive uncertainty of these data, derived from local BNNs, to construct feature distributions. These distributions are then provided to clients for fine-tuning the global distribution, resulting in personalized priors. In addition, to ensure optimal integration of local and global data insights, we design an adaptive ζ strategy in the local objective function to balance the log-likelihood estimation term and the KL divergence term. We provide theoretical analysis regarding the upper bound of the averaged generalization error for the proposed pFedBL and experimental results demonstrate its effectiveness on three datasets under different problem settings.