  Federated learning (FL for simplification) is a distributed machine learning
technique that utilizes global servers and collaborative clients to achieve
privacy-preserving global model training without direct data sharing. However,
heterogeneous data problem, as one of FL's main problems, makes it difficult
for the global model to perform effectively on each client's local data. Thus,
personalized federated learning (PFL for simplification) aims to improve the
performance of the model on local data as much as possible. Bayesian learning,
where the parameters of the model are seen as random variables with a prior
assumption, is a feasible solution to the heterogeneous data problem due to the
tendency that the more local data the model use, the more it focuses on the
local data, otherwise focuses on the prior. When Bayesian learning is applied
to PFL, the global model provides global knowledge as a prior to the local
training process. In this paper, we employ Bayesian learning to model PFL by
assuming a prior in the scaled exponential family, and therefore propose
pFedBreD, a framework to solve the problem we model using Bregman divergence
regularization. Empirically, our experiments show that, under the prior
assumption of the spherical Gaussian and the first order strategy of mean
selection, our proposal significantly outcompetes other PFL algorithms on
multiple public benchmarks.
