Hierarchical Federated Learning (HFL) is a distributed machine learning paradigm tailored for multi-tiered computation architectures, which supports massive access of devices' models simultaneously. To enable efficient HFL, it is crucial to design suitable incentive mechanisms to ensure that devices actively participate in local training. However, there are few studies on incentive mechanism design for HFL. In this paper, we design two-level incentive mechanisms for the HFL with a two-tiered computing structure to encourage the participation of entities in each tier in the HFL training. In the lower-level game, we propose a coalition formation game to joint optimize the edge association and bandwidth allocation problem, and obtain efficient coalition partitions by the proposed preference rule, which can be proven to be stable by exact potential game. In the upper-level game, we design the Stackelberg game algorithm, which not only determines the optimal number of edge aggregations for edge servers to maximize their utility, but also optimize the unit reward provided for the edge aggregation performance to ensure the interests of cloud servers. Furthermore, numerical results indicate that the proposed algorithms can achieve better performance than the benchmark schemes.

翻译：分层联邦学习是一种针对多层计算架构设计的分布式机器学习范式，支持海量设备模型的同时接入。为实现高效的分层联邦学习，设计合理的激励机制以确保设备积极参与本地训练至关重要。然而，目前针对分层联邦学习激励机制设计的研究尚不充分。本文针对具有两层计算结构的分层联邦学习，设计了两级激励机制以鼓励各层级实体参与训练。在底层博弈中，我们提出联盟形成博弈联合优化边缘关联与带宽分配问题，通过所提出的偏好规则获得高效的联盟划分，并利用精确势博弈证明其稳定性。在顶层博弈中，我们设计了斯塔克尔伯格博弈算法，该算法不仅能够确定边缘服务器最优的边缘聚合次数以最大化其效用，还能优化为边缘聚合性能提供的单位奖励，从而保障云服务器的利益。数值结果表明，所提算法相比基准方案能实现更优性能。