  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.
