Vertical Federated Learning (VFL) has emerged as a popular machine learning paradigm, enabling model training across the data and the task parties with different features about the same user set while preserving data privacy. In production environment, VFL usually involves one task party and one data party. Fair and economically efficient feature trading is crucial to the commercialization of VFL, where the task party is considered as the data consumer who buys the data party's features. However, current VFL feature trading practices often price the data party's data as a whole and assume transactions occur prior to the performing VFL. Neglecting the performance gains resulting from traded features may lead to underpayment and overpayment issues. In this study, we propose a bargaining-based feature trading approach in VFL to encourage economically efficient transactions. Our model incorporates performance gain-based pricing, taking into account the revenue-based optimization objectives of both parties. We analyze the proposed bargaining model under perfect and imperfect performance information settings, proving the existence of an equilibrium that optimizes the parties' objectives. Moreover, we develop performance gain estimation-based bargaining strategies for imperfect performance information scenarios and discuss potential security issues and solutions. Experiments on three real-world datasets demonstrate the effectiveness of the proposed bargaining model.

翻译：纵向联邦学习（VFL）已成为一种流行的机器学习范式，能够在保护数据隐私的前提下，利用同一用户集的不同特征在数据方和任务方之间进行模型训练。在实际生产环境中，VFL通常涉及一个任务方和一个数据方。公平且经济高效的特征交易对于VFL的商业化至关重要，其中任务方被视为购买数据方特征的数据消费者。然而，当前的VFL特征交易实践通常将数据方的数据整体定价，并假设交易发生在执行VFL之前。忽视交易特征带来的性能增益可能导致支付不足或过度支付问题。在本研究中，我们提出了一种基于谈判的VFL特征交易方法，以促进经济高效的交易。该模型融入了基于性能增益的定价机制，并考虑双方基于收益的优化目标。我们在完全和不完全性能信息设置下分析了所提出的谈判模型，证明了存在能够优化双方目标的均衡。此外，针对不完全性能信息场景，我们开发了基于性能增益估计的谈判策略，并讨论了潜在的安全问题及解决方案。在三个真实数据集上的实验证明了所提出谈判模型的有效性。