Abstract: In today's society with the growing demand for privacy protection, federated learning is receiving widespread attention. However, in federated learning, it is difficult for the server to supervise the behavior of clients, so the existence of lazy clients poses a potential threat to the performance and fairness of federated learning. The research on how to deal with the problem of efficiently and accurately identifying lazy clients was conducted, and a proof-of-work solution based on backdoors was proposed, referred to as FedBD. The server specifies an additional backdoor task that is easier to detect for the client participating in federated learning. The client trains the backdoor task based on the original training task, and the server indirectly supervises the client's behavior through the training status of the backdoor task. Experiments show that FedBD has certain advantages over the classic federated averaging algorithm (FedAvg) and the advanced GTG-Shapley on data sets such as MNIST and CIFAR10. When the proportion of lazy clients is 15%, the accuracy of test set can be improved by more than 10 percentage points compared with FedAvg, and the accuracy is improved by 2 percentage points compared with GTG-Shapley. Moreover, the average training time of FedBD is only 11.8% of that of GTG-Shapley, and the accuracy of FedBD in identifying lazy clients can exceed 99% when the proportion of lazy clients is 10%. FedBD better solves the problem of lazy clients being difficult to monitor.

Key words: federated learning, backdoor, lazy client, proof of work, data heterogeneity

摘要： 在对隐私保护的需求不断增长的当今社会，联邦学习正受到广泛关注。然而，在联邦学习中，服务器难监管客户端的行为，致使懒惰客户端的存在为联邦学习的表现与公平性带来了潜在威胁。针对如何高效又准确辨别懒惰客户端的问题展开研究，提出设置基于后门的工作证明方案，简称为FedBD。服务器为参与联邦学习的客户端额外指定更易检测的后门任务，客户端在训练原任务基础上训练后门任务，服务器通过后门任务的训练情况间接监管客户端行为。实验结果表明，在MNIST、CIFAR10等数据集上，相较于经典联邦平均算法(FedAvg)和先进的GTG-Shapley算法，FedBD有一定优势，在懒惰客户端占比设置为15%时，对比FedAvg准确率提升可达10个百分点以上，对比GTG-Shapley准确率提升约2个百分点。而且FedBD平均训练时间仅为GTG-Shapley的11.8%，在懒惰客户端占比10%时辨别懒惰客户端的准确率可超过99%，较好解决了懒惰客户端难以监管的问题。

关键词: 联邦学习, 后门, 懒惰客户端, 工作证明, 数据异构