Federated learning is a distributed machine learning system that uses participants' data to train an improved global model. In federated learning, participants cooperatively train a global model, and they will receive the global model and payments. Rational participants try to maximize their individual utility, and they will not input their high-quality data truthfully unless they are provided with satisfactory payments based on their data quality. Furthermore, federated learning benefits from the cooperative contributions of participants. Accordingly, how to establish an incentive mechanism that both incentivizes inputting data truthfully and promotes stable cooperation has become an important issue to consider. In this paper, we introduce a data sharing game model for federated learning and employ game-theoretic approaches to design a core-selecting incentive mechanism by utilizing a popular concept in cooperative games, the core. In federated learning, the core can be empty, resulting in the core-selecting mechanism becoming infeasible. To address this, our core-selecting mechanism employs a relaxation method and simultaneously minimizes the benefits of inputting false data for all participants. However, this mechanism is computationally expensive because it requires aggregating exponential models for all possible coalitions, which is infeasible in federated learning. To address this, we propose an efficient core-selecting mechanism based on sampling approximation that only aggregates models on sampled coalitions to approximate the exact result. Extensive experiments verify that the efficient core-selecting mechanism can incentivize inputting high-quality data and stable cooperation, while it reduces computational overhead compared to the core-selecting mechanism.

翻译：联邦学习是一种利用参与者数据训练改进全局模型的分布式机器学习系统。在联邦学习中，参与者协作训练全局模型，并据此获得模型和报酬。理性的参与者追求个体效用最大化，除非基于数据质量获得满意报酬，否则不会如实提供高质量数据。此外，联邦学习得益于参与者的协作贡献。因此，如何建立既能激励如实输入数据又能促进稳定合作的激励机制成为重要议题。本文引入联邦学习数据共享博弈模型，并采用博弈论方法，利用合作博弈中核这一经典概念设计了核心选择激励机制。在联邦学习中，核可能为空，导致核心选择机制不可行。为此，我们的核心选择机制采用松弛方法，同时最小化所有参与者输入虚假数据的收益。然而，该机制计算开销巨大，因其需聚合所有可能联盟的指数级模型，这在联邦学习中不可行。为解决此问题，我们提出基于采样近似的高效核心选择机制，仅对采样联盟进行模型聚合以近似精确结果。大量实验证明，该高效核心选择机制既能激励高质量数据输入与稳定合作，又能相比核心选择机制降低计算开销。