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DualGFL: Federated Learning with a Dual-Level Coalition-Auction Game

Xiaobing Chen, Xiangwei Zhou, Songyang Zhang, Mingxuan Sun

TL;DR

DualGFL tackles the incentive design in federated learning by introducing a dual-level game that combines a lower-level hedonic coalition formation with an auction-based upper level. The framework leverages a Pareto-Optimal Partitioning algorithm and a multi-attribute, resource-constrained auction to maximize both server utility and client welfare, with equilibrium bidding analyzed for coalitions. Empirical results on non-IID real-world datasets show significant gains in server and client utilities and competitive accuracy compared to single-level baselines. The approach offers a scalable, principled mechanism for joint economic efficiency and data utility in hierarchical federated learning.

Abstract

Despite some promising results in federated learning using game-theoretical methods, most existing studies mainly employ a one-level game in either a cooperative or competitive environment, failing to capture the complex dynamics among participants in practice. To address this issue, we propose DualGFL, a novel Federated Learning framework with a Dual-level Game in cooperative-competitive environments. DualGFL includes a lower-level hedonic game where clients form coalitions and an upper-level multi-attribute auction game where coalitions bid for training participation. At the lower-level DualGFL, we introduce a new auction-aware utility function and propose a Pareto-optimal partitioning algorithm to find a Pareto-optimal partition based on clients' preference profiles. At the upper-level DualGFL, we formulate a multi-attribute auction game with resource constraints and derive equilibrium bids to maximize coalitions' winning probabilities and profits. A greedy algorithm is proposed to maximize the utility of the central server. Extensive experiments on real-world datasets demonstrate DualGFL's effectiveness in improving both server utility and client utility.

DualGFL: Federated Learning with a Dual-Level Coalition-Auction Game

TL;DR

DualGFL tackles the incentive design in federated learning by introducing a dual-level game that combines a lower-level hedonic coalition formation with an auction-based upper level. The framework leverages a Pareto-Optimal Partitioning algorithm and a multi-attribute, resource-constrained auction to maximize both server utility and client welfare, with equilibrium bidding analyzed for coalitions. Empirical results on non-IID real-world datasets show significant gains in server and client utilities and competitive accuracy compared to single-level baselines. The approach offers a scalable, principled mechanism for joint economic efficiency and data utility in hierarchical federated learning.

Abstract

Despite some promising results in federated learning using game-theoretical methods, most existing studies mainly employ a one-level game in either a cooperative or competitive environment, failing to capture the complex dynamics among participants in practice. To address this issue, we propose DualGFL, a novel Federated Learning framework with a Dual-level Game in cooperative-competitive environments. DualGFL includes a lower-level hedonic game where clients form coalitions and an upper-level multi-attribute auction game where coalitions bid for training participation. At the lower-level DualGFL, we introduce a new auction-aware utility function and propose a Pareto-optimal partitioning algorithm to find a Pareto-optimal partition based on clients' preference profiles. At the upper-level DualGFL, we formulate a multi-attribute auction game with resource constraints and derive equilibrium bids to maximize coalitions' winning probabilities and profits. A greedy algorithm is proposed to maximize the utility of the central server. Extensive experiments on real-world datasets demonstrate DualGFL's effectiveness in improving both server utility and client utility.

Paper Structure

This paper contains 19 sections, 2 theorems, 19 equations, 6 figures, 2 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. System Model
  4. Hierarchical Federated Learning
  5. Cost Model
  6. Dual-Level Game Federated Learning
  7. Architecture
  8. Lower-Level Coalition Formation Game
  9. Hedonic Game
  10. Auction-Aware Preference Profile Generation
  11. Pareto-Optimal Partitioning Algorithm
  12. Upper-Level Multi-Attribute Auction with Resource Constraints
  13. Multi-Attribute Auction Model
  14. Equilibrium Bids of Coalitions
  15. Score Maximization Problem
  16. ...and 4 more sections

Key Result

Theorem 1

(Pareto-Optimal Partition) Let $(\mathcal{N}, \mathcal{R}^{\top})$ and $(\mathcal{N}, \mathcal{R}^{\bot})$ represent hedonic games where $\mathcal{R}^{\bot} \leq \mathcal{R}^{\top}$, which means that $\mathcal{R}^{\top}$ has some preferences that are more strict than the ones in $\mathcal{R}^{\bot}$

Figures (6)

  • Figure 1: DualGFL architecture.
  • Figure 2: Training dynamics of key metrics. (a), (b), (c), and (d) show the cumulative average of client quality, coalition quality, client payoff, and client utility, respectively.
  • Figure 3: Impact of max size $|S|_{max}$ on the performance of the coalition selection. (a) and (b) show the performance of DualGFL and DualGFLStat, respectively.
  • Figure A-1: Training dynamics of key metrics in FMNIST (0.6) setting.
  • Figure A-2: Training dynamics of key metrics in EMNIST (0.1) setting.
  • ...and 1 more figures

Theorems & Definitions (7)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Theorem 1
  • Theorem 2
  • proof