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In this paper, federated learning (FL) over wireless networks isinvestigated. In each communication round, a subset of devices is selected toparticipate in the aggregation with limited time and energy. In order tominimize the convergence time, global loss and latency are jointly consideredin a Stackelberg game based framework. Specifically, age of information (AoI)based device selection is considered at leader-level as a global lossminimization problem, while sub-channel assignment, computational resourceallocation, and power allocation are considered at follower-level as a latencyminimization problem. By dividing the follower-level problem into twosub-problems, the best response of the follower is obtained by a monotonicoptimization based resource allocation algorithm and a matching basedsub-channel assignment algorithm. By deriving the upper bound of convergencerate, the leader-level problem is reformulated, and then a list based deviceselection algorithm is proposed to achieve Stackelberg equilibrium. Simulationresults indicate that the proposed device selection scheme outperforms otherschemes in terms of the global loss, and the developed algorithms cansignificantly decrease the time consumption of computation and communication.

Age of Information in Federated Learning over Wireless Networks