Bayesian Federated Learning (FL) has been recently introduced to provide well-calibrated Machine Learning (ML) models quantifying the uncertainty of their predictions. Despite their advantages compared to frequentist FL setups, Bayesian FL tools implemented over decentralized networks are subject to high communication costs due to the iterated exchange of local posterior distributions among cooperating devices. Therefore, this paper proposes a communication-efficient decentralized Bayesian FL policy to reduce the communication overhead without sacrificing final learning accuracy and calibration. The proposed method integrates compression policies and allows devices to perform multiple optimization steps before sending the local posterior distributions. We integrate the developed tool in an Industrial Internet of Things (IIoT) use case where collaborating nodes equipped with autonomous radar sensors are tasked to reliably localize human operators in a workplace shared with robots. Numerical results show that the developed approach obtains highly accurate yet well-calibrated ML models compatible with the ones provided by conventional (uncompressed) Bayesian FL tools while substantially decreasing the communication overhead (i.e., up to 99%). Furthermore, the proposed approach is advantageous when compared with state-of-the-art compressed frequentist FL setups in terms of calibration, especially when the statistical distribution of the testing dataset changes.

翻译：贝叶斯联邦学习近期被引入，以提供能够量化预测不确定性的校准良好的机器学习模型。尽管与频率学派联邦学习设置相比具有优势，但在去中心化网络上实现的贝叶斯联邦学习工具由于合作设备之间反复交换局部后验分布，面临较高的通信成本。为此，本文提出一种通信高效的去中心化贝叶斯联邦学习策略，在不牺牲最终学习精度和校准性的前提下降低通信开销。所提方法整合了压缩策略，并允许设备在发送局部后验分布之前执行多次优化步骤。我们将该工具集成于一个工业物联网用例中：配备自主雷达传感器的协作节点需可靠定位与机器人共享工作空间中的人类操作员。数值结果表明，所提方法能够获得与常规（未压缩）贝叶斯联邦学习工具兼容的高精度且校准良好的机器学习模型，同时显著降低通信开销（最高达99%）。此外，与现有最先进的压缩频率学派联邦学习设置相比，所提方法在校准性方面更具优势，尤其在测试数据集统计分布发生变化时。