In recent years, there has been a significant increase in attention towards designing incentive mechanisms for federated learning (FL). Tremendous existing studies attempt to design the solutions using various approaches (e.g., game theory, reinforcement learning) under different settings. Yet the design of incentive mechanism could be significantly biased in that clients' performance in many applications is stochastic and hard to estimate. Properly handling this stochasticity motivates this research, as it is not well addressed in pioneering literature. In this paper, we focus on cross-device FL and propose a multi-level FL architecture under the real scenarios. Considering the two properties of clients' situations: uncertainty, correlation, we propose FL Incentive Mechanism based on Portfolio theory (FL-IMP). As far as we are aware, this is the pioneering application of portfolio theory to incentive mechanism design aimed at resolving FL resource allocation problem. In order to more accurately reflect practical FL scenarios, we introduce the Federated Learning Agent-Based Model (FL-ABM) as a means of simulating autonomous clients. FL-ABM enables us to gain a deeper understanding of the factors that influence the system's outcomes. Experimental evaluations of our approach have extensively validated its effectiveness and superior performance in comparison to the benchmark methods.

翻译：近年来，联邦学习激励机制设计受到广泛关注。现有大量研究尝试在不同设定下（如博弈论、强化学习）采用多种方法设计解决方案。然而，激励机制设计可能存在显著偏差，因为许多应用中客户端的性能具有随机性且难以准确评估。妥善处理这种随机性是本研究的主要动机，因为现有开创性文献尚未充分解决该问题。本文聚焦跨设备联邦学习场景，提出一种真实环境下的多层次联邦学习架构。考虑到客户端状态的两个特性——不确定性与相关性，我们提出了基于投资组合理论的联邦学习激励机制。据我们所知，这是首次将投资组合理论应用于激励机制设计以解决联邦学习资源分配问题。为更精确地反映实际联邦学习场景，我们引入基于智能体的联邦学习模型作为模拟自治客户端的方法。该模型使我们能够更深入地理解影响系统结果的关键因素。实验评估充分验证了所提方法的有效性，其性能显著优于基准方法。