Federated learning (FL) is a promising framework for learning from distributed data while maintaining privacy. The development of efficient FL algorithms encounters various challenges, including heterogeneous data and systems, limited communication capacities, and constrained local computational resources. Recently developed FedADMM methods show great resilience to both data and system heterogeneity. However, they still suffer from performance deterioration if the hyperparameters are not carefully tuned. To address this issue, we propose an inexact and self-adaptive FedADMM algorithm, termed FedADMM-InSa. First, we design an inexactness criterion for the clients' local updates to eliminate the need for empirically setting the local training accuracy. This inexactness criterion can be assessed by each client independently based on its unique condition, thereby reducing the local computational cost and mitigating the undesirable straggle effect. The convergence of the resulting inexact ADMM is proved under the assumption of strongly convex loss functions. Additionally, we present a self-adaptive scheme that dynamically adjusts each client's penalty parameter, enhancing algorithm robustness by mitigating the need for empirical penalty parameter choices for each client. Extensive numerical experiments on both synthetic and real-world datasets are conducted. As validated by some numerical tests, our proposed algorithm can reduce the clients' local computational load significantly and also accelerate the learning process compared to the vanilla FedADMM.

翻译：联邦学习（FL）是一种在保护隐私的同时从分布式数据中学习的富有前景的框架。高效FL算法的开发面临诸多挑战，包括异构数据与系统、有限的通信能力以及受限的本地计算资源。近期提出的FedADMM方法对数据和系统异构性均展现出很强的鲁棒性。然而，若超参数未仔细调整，这些方法仍会出现性能退化。为解决此问题，本文提出一种不精确且自适应的FedADMM算法，称为FedADMM-InSa。首先，我们为客户端本地更新设计了一个不精确性准则，从而无需经验性地设定本地训练精度。该不精确性准则可由每个客户端根据其自身条件独立评估，进而降低本地计算开销并缓解不利的掉队效应。在强凸损失函数假设下，我们证明了所得到的不精确ADMM的收敛性。此外，我们提出了一种自适应方案，可动态调整每个客户端的惩罚参数，通过减少对每个客户端惩罚参数经验性选择的需求来增强算法鲁棒性。在合成数据集和真实世界数据集上进行了大量数值实验。数值测试验证表明，与原始FedADMM相比，本文算法可显著降低客户端本地计算负载，并加速学习过程。