Federated learning, a decentralized approach to machine learning, faces significant challenges such as extensive communication overheads, slow convergence, and unstable improvements. These challenges primarily stem from the gradient variance due to heterogeneous client data distributions. To address this, we introduce a novel Networked Control Variates (FedNCV) framework for Federated Learning. We adopt the REINFORCE Leave-One-Out (RLOO) as a fundamental control variate unit in the FedNCV framework, implemented at both client and server levels. At the client level, the RLOO control variate is employed to optimize local gradient updates, mitigating the variance introduced by data samples. Once relayed to the server, the RLOO-based estimator further provides an unbiased and low-variance aggregated gradient, leading to robust global updates. This dual-side application is formalized as a linear combination of composite control variates. We provide a mathematical expression capturing this integration of double control variates within FedNCV and present three theoretical results with corresponding proofs. This unique dual structure equips FedNCV to address data heterogeneity and scalability issues, thus potentially paving the way for large-scale applications. Moreover, we tested FedNCV on six diverse datasets under a Dirichlet distribution with {\alpha} = 0.1, and benchmarked its performance against six SOTA methods, demonstrating its superiority.

翻译：联邦学习作为一种去中心化的机器学习方法，面临通信开销大、收敛速度慢和优化效果不稳定等重大挑战。这些困难主要源于客户端数据分布异质性导致的梯度方差。为此，我们提出了一种新颖的基于网络化控制变量（FedNCV）的联邦学习框架。在该框架中，我们采用REINFORCE留一法（RLOO）作为基础控制变量单元，并将其部署在客户端和服务端两个层面。在客户端层面，通过RLOO控制变量优化本地梯度更新，有效抑制数据采样引入的方差；而传递至服务端后，基于RLOO的估计器进一步提供无偏且低方差的聚合梯度，从而保证全局更新的稳健性。这种双边应用被形式化为复合控制变量的线性组合。我们给出了FedNCV中双重控制变量整合的数学表达式，并提供了三个理论结果及其相应证明。这种独特的双重结构使FedNCV能够有效应对数据异质性和可扩展性问题，从而为大规模应用开辟了新路径。此外，我们在Dirichlet分布（α=0.1）条件下，基于六个不同数据集对FedNCV进行测试，并将其性能与六种当前最优方法进行了对比基准测试，结果证明了其优越性。