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Federated learning (FL) leverages the private data and computing power of multiple clients to collaboratively train a global model. Many existing FL algorithms over wireless networks adopting synchronous model aggregation suffer from the straggler issue, due to the heterogeneity of local computing power and channel conditions. To address this issue, we in this paper advocate an asynchronous FL framework with adaptive client selection for training latency minimization, taking into account the client availability and long-term fairness. We consider a practical scenario, where the channel conditions and the locally available computing power are not known in prior. This makes the client selection problem challenging, as the training latency consists of the uplink/downlink transmission time and the local training time. To this end, we tackle the asynchronous client selection problem in an online manner by converting …