Abstract: Federated learning effectively solves the problem of isolated data island,but there are some challenges.Firstly,the training nodes of federated learning have a large hardware heterogeneity,which has an impact on the training speed and model performance.The existing researches mainly focus on federated optimization,but most methods do not solve the problem of resource waste caused by the different computing time of each node in synchronous communication mode.In addition,most of the training nodes in federated learning are mobile devices,so the poor network environment leads to high communication overhead and serious network bottlenecks.Existing methods reduce the communication overhead by compressing the gradient uploaded by the training nodes,but inevitably bring the loss of model performance and it is difficult to achieve a good balance between quality and speed.To solve these problems,at the computing stage,this paper proposes adap-tive federated averaging(AFA),which adaptatively coordinates the local iteration according to the hardware performance of each node,minimizes the idle time of waiting for global gradient download and improves the computational efficiency of federated learning.In the communication stage,it proposes double sparsification(DS) to minimize the communication overhead by gradient sparsification on the training node and parameter server.In addition,each training node compensates the error according to the lost value of the local gradient and the global gra-dient,and reduces the communication cost greatly in exchange for lower model performance loss.Experimental results on the image classification dataset and the spatio-temporal prediction dataset prove that the proposed method can effectively improve the training acceleration ratio,and is also helpful to the model performance.

Key words: Federated learning, Distributed machine learning, Parallel computing, Parameter synchronization, Sparse representation