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Incentive-Compatible Federated Learning with Stackelberg Game Modeling

Simin Javaherian, Bryce Turney, Li Chen, Nian-Feng Tzeng

TL;DR

FLamma addresses fairness in heterogeneous federated learning by formulating server–client interactions as an adaptive gamma-based Stackelberg game, where the server (leader) tunes a decay factor $\gamma$ and clients (followers) choose local epochs $\tau_i$ to maximize their utilities. The framework derives client best responses and server optimality conditions, proving equilibrium existence and the IR property, and provides a convergence bound under standard FL assumptions. Empirical results on IID and non-IID data (MNIST, FMNIST, CIFAR10) show dramatically reduced accuracy variance across clients with competitive global accuracy, outperforming FedAvg, FedProx, q-FFL, and Incentivization in fairness and robustness. The approach offers a principled, incentive-compatible mechanism for fair resource allocation and stable convergence in diverse FL environments, with potential extensions via RL-based hyperparameter optimization.

Abstract

Federated Learning (FL) has gained prominence as a decentralized machine learning paradigm, allowing clients to collaboratively train a global model while preserving data privacy. Despite its potential, FL faces significant challenges in heterogeneous environments, where varying client resources and capabilities can undermine overall system performance. Existing approaches primarily focus on maximizing global model accuracy, often at the expense of unfairness among clients and suboptimal system efficiency, particularly in non-IID (non-Independent and Identically Distributed) settings. In this paper, we introduce FLamma, a novel Federated Learning framework based on adaptive gamma-based Stackelberg game, designed to address the aforementioned limitations and promote fairness. Our approach allows the server to act as the leader, dynamically adjusting a decay factor while clients, acting as followers, optimally select their number of local epochs to maximize their utility. Over time, the server incrementally balances client influence, initially rewarding higher-contributing clients and gradually leveling their impact, driving the system toward a Stackelberg Equilibrium. Extensive simulations on both IID and non-IID datasets show that our method significantly improves fairness in accuracy distribution without compromising overall model performance or convergence speed, outperforming traditional FL baselines.

Incentive-Compatible Federated Learning with Stackelberg Game Modeling

TL;DR

FLamma addresses fairness in heterogeneous federated learning by formulating server–client interactions as an adaptive gamma-based Stackelberg game, where the server (leader) tunes a decay factor and clients (followers) choose local epochs to maximize their utilities. The framework derives client best responses and server optimality conditions, proving equilibrium existence and the IR property, and provides a convergence bound under standard FL assumptions. Empirical results on IID and non-IID data (MNIST, FMNIST, CIFAR10) show dramatically reduced accuracy variance across clients with competitive global accuracy, outperforming FedAvg, FedProx, q-FFL, and Incentivization in fairness and robustness. The approach offers a principled, incentive-compatible mechanism for fair resource allocation and stable convergence in diverse FL environments, with potential extensions via RL-based hyperparameter optimization.

Abstract

Federated Learning (FL) has gained prominence as a decentralized machine learning paradigm, allowing clients to collaboratively train a global model while preserving data privacy. Despite its potential, FL faces significant challenges in heterogeneous environments, where varying client resources and capabilities can undermine overall system performance. Existing approaches primarily focus on maximizing global model accuracy, often at the expense of unfairness among clients and suboptimal system efficiency, particularly in non-IID (non-Independent and Identically Distributed) settings. In this paper, we introduce FLamma, a novel Federated Learning framework based on adaptive gamma-based Stackelberg game, designed to address the aforementioned limitations and promote fairness. Our approach allows the server to act as the leader, dynamically adjusting a decay factor while clients, acting as followers, optimally select their number of local epochs to maximize their utility. Over time, the server incrementally balances client influence, initially rewarding higher-contributing clients and gradually leveling their impact, driving the system toward a Stackelberg Equilibrium. Extensive simulations on both IID and non-IID datasets show that our method significantly improves fairness in accuracy distribution without compromising overall model performance or convergence speed, outperforming traditional FL baselines.
Paper Structure (16 sections, 23 equations, 3 figures, 1 table, 1 algorithm)

This paper contains 16 sections, 23 equations, 3 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background and Related works
  3. Preliminaries
  4. Federated Learning
  5. Game Theory and Stackelberg Games
  6. Design of FLamma
  7. Overview
  8. Game Strategy
  9. Stackelberg Equilibrium
  10. Convergence Analysis
  11. Experiments and Results
  12. Setup
  13. Evaluation Metrics
  14. Performance Results and Discussion
  15. Limitation and Future Work
  16. ...and 1 more sections

Figures (3)

  • Figure 1: Overview of FLamma, an adaptive gamma-based game theoretic framework for fair federated learning.
  • Figure 2: Comparison of the FLamma with the baselines including FedAvg, FedProx, q-FFL, and Incentivization in terms of accuracy, and accuracy variance on IID dataset.
  • Figure 3: Comparison of the FLamma with the baselines including FedAvg, FedProx, q-FFL, and Incentivization in terms of accuracy, and accuracy variance on non-IID dataset.