Beyond Staleness Decay: History-Enhanced Residual Acceleration in Asynchronous Federated Learning

Asynchronous federated learning produces a stream of client updates computed from stale model snapshots. We introduce History-Enhanced Residual Acceleration (HERA), a server-side method that reuses this stream as a short residual history for Anderson mixing. Lagged RMS stabilization balances the residual geometry, while a base-anchored update controls the full displacement of each history proposal. Our analysis separates base-update drift, delay, history amplitude, and client-selection bias. With bounded delay, uniform sampling, and a stepsize-scaled anchor, local-SGD residuals attain the $O(K^{-1/2})$ nonconvex stationarity rate; nonuniform arrivals and fixed anchors contribute explicit residual terms. A local error bound relates proposal quality to residual fitting, map conditioning, and evaluation mismatch. A four-way MNIST ablation examines the interaction between RMS stabilization and history correction, with their combination improving mean final accuracy over RMS alone in all five settings. Across ten CIFAR scenarios, HERA attains the highest mean final validation accuracy in eight, including all six non-IID settings.