Federated learning (FL) is an emerging distributed training paradigm that aims to learn a common global model without exchanging or transferring the data that are stored locally at different clients. The Federated Averaging (FedAvg)-based algorithms have gained substantial popularity in FL to reduce the communication overhead, where each client conducts multiple localized iterations before communicating with a central server. In this paper, we focus on FL where the clients have diverse computation and/or communication capabilities. Under this circumstance, FedAvg can be less efficient since it requires all clients that participate in the global aggregation in a round to initiate iterations from the latest global model, and thus the synchronization among fast clients and straggler clients can severely slow down the overall training process. To address this issue, we propose an efficient asynchronous federated learning (AFL) framework called Delayed Federated Averaging (DeFedAvg). In DeFedAvg, the clients are allowed to perform local training with different stale global models at their own paces. Theoretical analyses demonstrate that DeFedAvg achieves asymptotic convergence rates that are on par with the results of FedAvg for solving nonconvex problems. More importantly, DeFedAvg is the first AFL algorithm that provably achieves the desirable linear speedup property, which indicates its high scalability. Additionally, we carry out extensive numerical experiments using real datasets to validate the efficiency and scalability of our approach when training deep neural networks.

我们提出了一种高效的异步联邦学习（AFL）框架，称为延迟联邦平均（DeFedAvg），通过在自己的速度上使用不同陈旧的全局模型，DeFedAvg可以达到与FedAvg相当的渐近收敛速率，同时也是第一个具有可证明的良好线性加速特性的AFL算法，从而表明其高可扩展性。

异步联邦学习中实现线性加速