Existing research has either adapted the Probably Approximately Correct (PAC) Bayesian framework for federated learning (FL) or used information-theoretic PAC-Bayesian bounds while introducing their theorems, but few considering the non-IID challenges in FL. Our work presents the first non-vacuous federated PAC-Bayesian bound tailored for non-IID local data. This bound assumes unique prior knowledge for each client and variable aggregation weights. We also introduce an objective function and an innovative Gibbs-based algorithm for the optimization of the derived bound. The results are validated on real-world datasets.

翻译：现有研究要么将概率近似正确（PAC）贝叶斯框架适配于联邦学习，要么在引入其定理的同时使用信息论PAC-贝叶斯界，但鲜有研究考虑联邦学习中的非同分布挑战。本文提出了首个针对非同分布局部数据的非空洞联邦PAC-贝叶斯界。该界限假设每个客户端具有独特的先验知识及可变的聚合权重。我们还引入一个目标函数和一种基于吉布斯采样的创新算法，用于优化所推导的界限。实验结果在真实数据集上得到了验证。