Federated learning (FL) leverages client-server communications to train global models on decentralized data. However, communication noise or errors can impair model accuracy. To address this problem, we propose a novel FL algorithm that enhances robustness against communication noise while also reducing communication load. We derive the proposed algorithm through solving the weighted least-squares (WLS) regression problem as an illustrative example. We first frame WLS regression as a distributed convex optimization problem over a federated network employing random scheduling for improved communication efficiency. We then apply the alternating direction method of multipliers (ADMM) to iteratively solve this problem. To counteract the detrimental effects of cumulative communication noise, we introduce a key modification by eliminating the dual variable and implementing a new local model update at each participating client. This subtle yet effective change results in using a single noisy global model update at each client instead of two, improving robustness against additive communication noise. Furthermore, we incorporate another modification enabling clients to continue local updates even when not selected by the server, leading to substantial performance improvements. Our theoretical analysis confirms the convergence of our algorithm in both mean and the mean-square senses, even when the server communicates with a random subset of clients over noisy links at each iteration. Numerical results validate the effectiveness of our proposed algorithm and corroborate our theoretical findings.

本研究针对联邦学习中的通信噪声问题，提出了一种新颖的算法，以增强模型的鲁棒性并减少通信负载。通过将加权最小二乘回归作为例子，采用交替方向乘子法（ADMM），该算法在每个参与客户端进行新型本地模型更新，从而显著改善了在噪声环境下的模型性能。这一方法及其理论分析展示了在随机客户端选择和噪音通信条件下的收敛性，以及其实际效果的有效性。

噪声鲁棒且资源高效的基于ADMM的联邦学习