Communication-Efficient Federated Learning via Fractional-Order Gradient Descent With Adaptive Momentum Under Non-IID Data

Abstract

Federated learning (FL) enables collaborative model training without centralized data sharing, yet its practical deployment is often hindered by slow convergence and excessive communication overhead, particularly under non-Independent and non-Identically Distributed (non-IID) data distributions. To address these challenges, this paper proposes Federated Fractional Order Gradient Descent with Adaptive Momentum (FedFOGDAM), a novel client-side optimization framework that integrates fractional-order gradients with adaptive momentum and bias correction to accelerate convergence and reduce the number of communication rounds (CRs) required for model convergence. By leveraging the memory effect of fractional-order calculus, FedFOGDAM stabilizes local updates and mitigates client drift, while adaptive momentum enhances update consistency across heterogeneous clients. We provide a rigorous convergence analysis under non-convex objectives, demonstrating improved convergence behavior compared to conventional integer-order optimizers. Extensive experiments on benchmark datasets under both IID and non-IID settings show that FedFOGDAM consistently achieves communication-efficient convergence and competitive accuracy.