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A Bargaining-based Approach for Feature Trading in Vertical Federated Learning

Yue Cui, Liuyi Yao, Zitao Li, Yaliang Li, Bolin Ding, Xiaofang Zhou

TL;DR

The paper targets economically efficient feature trading in vertical federated learning (VFL) by introducing a bargaining-based mechanism where the data party and task party negotiate pricing based on the expected performance gain $\Delta G$ from feature bundles. The authors analyze both perfect and imperfect performance information settings, proving the existence of an equilibrium and proposing estimation-based strategies when $\Delta G$ is uncertain. They integrate a performance-gain pricing function to compute payments $R_d$ and $R_t$, incorporate bargaining costs $C(T)$, and discuss security considerations for privacy-preserving exchanges, with experimental validation on Titanic, Credit, and Adult datasets demonstrating improved alignment with data-party reserves and higher net profits. This work offers a foundational approach to data valuation and incentive design in privacy-preserving VFL markets, enabling more economically efficient collaborations between data owners and task owners.

Abstract

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.

A Bargaining-based Approach for Feature Trading in Vertical Federated Learning

TL;DR

The paper targets economically efficient feature trading in vertical federated learning (VFL) by introducing a bargaining-based mechanism where the data party and task party negotiate pricing based on the expected performance gain from feature bundles. The authors analyze both perfect and imperfect performance information settings, proving the existence of an equilibrium and proposing estimation-based strategies when is uncertain. They integrate a performance-gain pricing function to compute payments and , incorporate bargaining costs , and discuss security considerations for privacy-preserving exchanges, with experimental validation on Titanic, Credit, and Adult datasets demonstrating improved alignment with data-party reserves and higher net profits. This work offers a foundational approach to data valuation and incentive design in privacy-preserving VFL markets, enabling more economically efficient collaborations between data owners and task owners.

Abstract

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.
Paper Structure (28 sections, 4 theorems, 13 equations, 4 figures, 4 tables, 1 algorithm)

This paper contains 28 sections, 4 theorems, 13 equations, 4 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminary
  3. The Bargaining-based VFL Market
  4. Assumptions
  5. Objectives of Participants
  6. Iterative Bargaining
  7. Perfect Performance Information
  8. Perfect Performance Information: Bargaining Analysis On The Data Party
  9. Perfect Performance Information: Bargaining Analysis On The Task Party
  10. Perfect Performance Information: Termination Conditions
  11. Perfect Performance Information: Bargaining Cost
  12. Extending to Imperfect Performance Information
  13. Performance Estimation
  14. Imperfect Performance Information: Bargaining Analysis On The Data Party
  15. Imperfect Performance Information: Bargaining Analysis On The Task Party
  16. ...and 13 more sections

Key Result

Theorem 3.1

There exists a quoted price $(p^*,P_0^*,P_h^*)$ that leads to the same bargaining result as $(p,P_0,P_h)$, i.e., the same offered feature bundle, the same performance gain, the same net profit for the task party and the same payment on the data party, while it satisfies $(P^*_h-P^*_0)/p^*=\Delta G$

Figures (4)

  • Figure 1: $\Delta G$v.s. the objective functions of the data party and the task party.
  • Figure 2: Bargaining results on the Titanic, Credit, and Adult datasets with Random Forest model. (a) Net profit v.s. bargaining rounds. (b) Payment v.s. bargaining rounds. (c) $\Delta G$v.s. bargaining rounds. (e) Final $p$ of each run of bargaining game v.s. the reserved price $p_l$ of the data parties target feature bundle. (f) Final $P_0$ of each run of bargaining game v.s. the reserved price $P_l$ of the data parties target feature bundle.
  • Figure 3: Bargaining results on the Titanic, Credit, and Adult datasets with 3-layer MLP model. Similar subfigure format as Figure \ref{['fig:per_false']}.
  • Figure 4: The MSE of $\Delta G$ estimation networks on two parties.

Theorems & Definitions (8)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Definition 2.4
  • Theorem 3.1
  • Lemma 3.1
  • Proposition 3.1
  • Proposition 3.2