Training latency is critical for the success of numerous intrigued applications ignited by federated learning (FL) over heterogeneous mobile devices. By revolutionarily overlapping local gradient transmission with continuous local computing, FL can remarkably reduce its training latency over homogeneous clients, yet encounter severe model staleness, model drifts, memory cost and straggler issues in heterogeneous environments. To unleash the full potential of overlapping, we propose, FedEx, a novel \underline{fed}erated learning approach to \underline{ex}pedite FL training over mobile devices under data, computing and wireless heterogeneity. FedEx redefines the overlapping procedure with staleness ceilings to constrain memory consumption and make overlapping compatible with participation selection (PS) designs. Then, FedEx characterizes the PS utility function by considering the latency reduced by overlapping, and provides a holistic PS solution to address the straggler issue. FedEx also introduces a simple but effective metric to trigger overlapping, in order to avoid model drifts. Experimental results show that compared with its peer designs, FedEx demonstrates substantial reductions in FL training latency over heterogeneous mobile devices with limited memory cost.
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