Stability-Enhanced Federated Learning with Accelerated Gradient

Federated Learning (FL) is a promising paradigm for distributed machine learning. However, FL often suffers from degraded generalization performance due to the inconsistency between local and global optimization objectives and client-side overfitting. In this paper, we provide a global-update stability analysis framework as an analytical tool to study generalization error and derive the stability bounds of mainstream FL optimization algorithms under non-convex settings. Our analyses reveal how the number of global update steps, data heterogeneity, and update rules influence their stability. We observe that momentum-based FL acceleration methods do not improve stability. To address this issue, we propose FedSEMA, a new FL algorithm that couples global momentum with a gradient-difference corrected Nesterov Accelerated Gradient (NAG) scheme and a hybrid proximal term to enhance stability. This design ensures updates follow a globally consistent descent direction while retaining the benefits of acceleration. Theoretical analysis shows that FedSEMA achieves an improved stability upper bound on non-i.i.d. datasets in the non-convex settings. Extensive experiments on real-world datasets demonstrate that FedSEMA significantly outperforms multiple baseline methods under standard FL settings, achieving faster convergence and state-of-the-art performance.