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Incentive Analysis for Agent Participation in Federated Learning

Lihui Yi, Xiaochun Niu, Ermin Wei

TL;DR

This work characterize the participation patterns and identify Nash equilibrium, revealing how data heterogeneity influences the equilibrium behavior—specifically, agents with similar data qualities will participate in FL as a group and derive the optimal social welfare strategy and show that it lies in a neighborhood of Nash equilibrium.

Abstract

Federated learning offers a decentralized approach to machine learning, where multiple agents collaboratively train a model while preserving data privacy. In this paper, we investigate the decision-making and equilibrium behavior in federated learning systems, where agents choose between participating in global training or conducting independent local training. The problem is first modeled as a stage game and then extended to a repeated game to analyze the long-term dynamics of agent participation. For the stage game, we characterize the participation patterns and identify Nash equilibrium, revealing how data heterogeneity influences the equilibrium behavior-specifically, agents with similar data qualities will participate in FL as a group. We also derive the optimal social welfare and show that it coincides with Nash equilibrium under mild assumptions. In the repeated game, we propose a privacy-preserving, computationally efficient myopic strategy. This strategy enables agents to make practical decisions under bounded rationality and converges to a neighborhood of Nash equilibrium of the stage game in finite time. By combining theoretical insights with practical strategy design, this work provides a realistic and effective framework for guiding and analyzing agent behaviors in federated learning systems.

Incentive Analysis for Agent Participation in Federated Learning

TL;DR

This work characterize the participation patterns and identify Nash equilibrium, revealing how data heterogeneity influences the equilibrium behavior—specifically, agents with similar data qualities will participate in FL as a group and derive the optimal social welfare strategy and show that it lies in a neighborhood of Nash equilibrium.

Abstract

Federated learning offers a decentralized approach to machine learning, where multiple agents collaboratively train a model while preserving data privacy. In this paper, we investigate the decision-making and equilibrium behavior in federated learning systems, where agents choose between participating in global training or conducting independent local training. The problem is first modeled as a stage game and then extended to a repeated game to analyze the long-term dynamics of agent participation. For the stage game, we characterize the participation patterns and identify Nash equilibrium, revealing how data heterogeneity influences the equilibrium behavior-specifically, agents with similar data qualities will participate in FL as a group. We also derive the optimal social welfare and show that it coincides with Nash equilibrium under mild assumptions. In the repeated game, we propose a privacy-preserving, computationally efficient myopic strategy. This strategy enables agents to make practical decisions under bounded rationality and converges to a neighborhood of Nash equilibrium of the stage game in finite time. By combining theoretical insights with practical strategy design, this work provides a realistic and effective framework for guiding and analyzing agent behaviors in federated learning systems.

Paper Structure

This paper contains 16 sections, 9 theorems, 8 equations, 2 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Stage Game
  3. Problem Formulation
  4. Nash Equilibrium
  5. type 1 (0-consecutive participation)
  6. type 2 ($k^*$-consecutive participation)
  7. Social Welfare Maximization
  8. Repeated Game
  9. Problem Formulation
  10. Subgame-Perfect Equilibrium
  11. Myopic Strategy
  12. Privacy-preserving design
  13. Decentralized decision-making
  14. Efficiency and practical convergence
  15. Bounded Rationality
  16. ...and 1 more sections

Key Result

Lemma 1

Assume $s^* =(s_1^*, \cdots, s_m^*)$ is an equilibrium of the stage game $\mathcal{G}$. Fix $i\in\{1,2,...,m\}$, if there exist $p,q\in \{1,2,...,m\}$ such that $p<i<q$ and $s_p^* = s_q^* = 1$, then $s_i^* = 1$.

Figures (2)

  • Figure 1: The relation between the number of participants in a type 2 equilibrium $k^*$ and the data separation $\Delta$. The following parameters are used for the plot: $m=25$, $n=100$, $a=790$.
  • Figure 2: Examples of the myopic strategy dynamics with two different initializations. We use parameters $m=20$, $n=100$, $a=790$. The number of FL participants of a type 2 equilibrium is $k^*=15$.

Theorems & Definitions (14)

  • Definition 1
  • Lemma 1
  • Definition 2
  • Definition 3
  • Theorem 1
  • Lemma 2
  • Theorem 2
  • Remark 1
  • Theorem 3
  • Lemma 3
  • ...and 4 more