Optimization-based techniques for federated learning (FL) often come with
prohibitive communication cost, as high dimensional model parameters need to be
communicated repeatedly between server and clients. In this paper, we follow a
Bayesian approach allowing to perform FL with one-shot communication, by
solving the global inference problem as a product of local client posteriors.
For models with multi-modal likelihoods, such as neural networks, a naive
application of this scheme is hampered, since clients will capture different
posterior modes, causing a destructive collapse of the posterior on the server
side. Consequently, we explore approximate inference in the function-space
representation of client posteriors, hence suffering less or not at all from
multi-modality. We show that distributed function-space inference is tightly
related to learning Bayesian pseudocoresets and develop a tractable Bayesian FL
algorithm on this insight. We show that this approach achieves prediction
performance competitive to state-of-the-art while showing a striking reduction
in communication cost of up to two orders of magnitude. Moreover, due to its
Bayesian nature, our method also delivers well-calibrated uncertainty
estimates.

基于优化的技术在联邦学习中通常具有高昂的通信成本，本文提出了一种基于贝叶斯方法的联邦学习算法，通过分布函数空间推断实现了仅需一次通信，并且在多模态条件下能够更好地进行近似推断，从而大大降低了通信成本。此算法在预测性能方面与最新技术水平相当，并能提供可靠的不确定性估计。