Federated learning (FL) serves as a data privacy-preserved machine learning paradigm, and realizes the collaborative model trained by distributed clients. To accomplish an FL task, the task publisher needs to pay financial incentives to the FL server and FL server offloads the task to the contributing FL clients. It is challenging to design proper incentives for the FL clients due to the fact that the task is privately trained by the clients. This paper aims to propose a contract theory based FL task training model towards minimizing incentive budget subject to clients being individually rational (IR) and incentive compatible (IC) in each FL training round. We design a two-dimensional contract model by formally defining two private types of clients, namely data quality and computation effort. To effectively aggregate the trained models, a contract-based aggregator is proposed. We analyze the feasible and optimal contract solutions to the proposed contract model. %Experimental results demonstrate that the proposed framework and contract model can effective improve the generation accuracy of FL tasks. Experimental results show that the generalization accuracy of the FL tasks can be improved by the proposed incentive mechanism where contract-based aggregation is applied.

翻译：联邦学习(FL)是数据保密的机器学习模式,实现了由分布式客户培训的协作模式。为了完成FL任务,任务出版商需要向FL服务器和FL服务器支付财政奖励,将任务卸下给FL客户;由于FL任务是由客户私下培训,因此很难为FL客户设计适当的奖励办法。本文件旨在提出基于合同理论的FL任务培训模式,以尽量减少奖励预算,条件是客户在每一轮FL培训中都具有个人理性和激励兼容性。我们设计了二维合同模式,正式界定了两类私人客户,即数据质量和计算工作。为了有效地综合经过培训的模型,提议了一个基于合同的聚合器。我们分析了拟议合同模式的可行和最佳合同解决办法。% 研究结果表明,拟议的框架和合同模式能够有效地提高FL任务的生成准确性。实验结果表明,拟议的奖励机制可以改进FL任务的普及性准确性,因为采用基于合同的总合。