Vertical federated learning (VFL) is a promising approach for collaboratively
training machine learning models using private data partitioned vertically
across different parties. Ideally in a VFL setting, the active party (party
possessing features of samples with labels) benefits by improving its machine
learning model through collaboration with some passive parties (parties
possessing additional features of the same samples without labels) in a privacy
preserving manner. However, motivating passive parties to participate in VFL
can be challenging. In this paper, we focus on the problem of allocating
incentives to the passive parties by the active party based on their
contributions to the VFL process. We formulate this problem as a variant of the
Nucleolus game theory concept, known as the Bankruptcy Problem, and solve it
using the Talmud's division rule. We evaluate our proposed method on synthetic
and real-world datasets and show that it ensures fairness and stability in
incentive allocation among passive parties who contribute their data to the
federated model. Additionally, we compare our method to the existing solution
of calculating Shapley values and show that our approach provides a more
efficient solution with fewer computations.

本文关注垂直联邦学习中的激励分配问题，将其视为 Nucleolus 博弈论概念的一种变体，利用 Talmud 的分割法则解决该问题。我们在合成数据集和真实数据集上评估了我们提出的方法，并展示其在为联邦模型做出贡献的被动方实现激励分配的公平性和稳定性。此外，我们与计算 Shapley 值的现有解决方案进行了比较，并展示了我们的方法在计算量更少的情况下提供了更高效的解决方案。