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A Communication-Efficient and Differentially-Private Distributed Generalized Nash Equilibrium Seeking Algorithm for Aggregative Games

Wenqing Zhao, Antai Xie, Yuchi Wu, Xinlei Yi, Xiaoqiang Ren

TL;DR

This work tackles distributed GNE seeking in aggregative games with coupling constraints under communication limits and privacy requirements. It introduces Algorithm 1, which fuses an event-triggered mechanism with stochastic compression to cut communication rounds and bits while preserving convergence to the exact GNE. Theoretical results establish almost-sure convergence under precise step-size conditions and prove $(0,\delta)$-differential privacy via a biased-but-unbiased compressor framework. Simulations on a multi-user energy platform validate the approach, showing robust convergence and favorable privacy-communication trade-offs. The framework offers a practical, scalable solution for privacy-preserving, communication-efficient distributed GNE in networked systems.

Abstract

This paper studies the distributed generalized Nash equilibrium seeking problem for aggregative games with coupling constraints, where each player optimizes its strategy depending on its local cost function and the estimated strategy aggregation. The information transmission in distributed networks may go beyond bandwidth capacity and eventuate communication bottlenecks. Therefore, we propose a novel communication-efficient distributed generalized Nash equilibrium seeking algorithm, in which the communication efficiency is improved by event-triggered communication and information compression methods. The proposed algorithm saves the transmitted rounds and bits of communication simultaneously. Specifically, by developing precise step size conditions, the proposed algorithm ensures provable convergence, and is proven to achieve $(0,δ)$-differential privacy with a stochastic quantization scheme. In the end, simulation results verify the effectiveness of the proposed algorithm.

A Communication-Efficient and Differentially-Private Distributed Generalized Nash Equilibrium Seeking Algorithm for Aggregative Games

TL;DR

This work tackles distributed GNE seeking in aggregative games with coupling constraints under communication limits and privacy requirements. It introduces Algorithm 1, which fuses an event-triggered mechanism with stochastic compression to cut communication rounds and bits while preserving convergence to the exact GNE. Theoretical results establish almost-sure convergence under precise step-size conditions and prove -differential privacy via a biased-but-unbiased compressor framework. Simulations on a multi-user energy platform validate the approach, showing robust convergence and favorable privacy-communication trade-offs. The framework offers a practical, scalable solution for privacy-preserving, communication-efficient distributed GNE in networked systems.

Abstract

This paper studies the distributed generalized Nash equilibrium seeking problem for aggregative games with coupling constraints, where each player optimizes its strategy depending on its local cost function and the estimated strategy aggregation. The information transmission in distributed networks may go beyond bandwidth capacity and eventuate communication bottlenecks. Therefore, we propose a novel communication-efficient distributed generalized Nash equilibrium seeking algorithm, in which the communication efficiency is improved by event-triggered communication and information compression methods. The proposed algorithm saves the transmitted rounds and bits of communication simultaneously. Specifically, by developing precise step size conditions, the proposed algorithm ensures provable convergence, and is proven to achieve -differential privacy with a stochastic quantization scheme. In the end, simulation results verify the effectiveness of the proposed algorithm.

Paper Structure

This paper contains 16 sections, 7 theorems, 38 equations, 2 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Formulation
  3. Problem Formulation
  4. Graph Theory
  5. Compression Method
  6. Event-triggered Mechanism
  7. Main Results
  8. Algorithm Design
  9. Convergence Analysis
  10. Differential Privacy Analysis
  11. Simulation
  12. Conclusion
  13. Appendix
  14. Proof of Lemma 5
  15. Proof of Theorem 1
  16. ...and 1 more sections

Key Result

Lemma 1

cominetti2012modern The fixed point $(\mathbf{x}^*, \mathbf{\lambda}^*)$ of (4) is also the GNE of Problem 1.

Figures (2)

  • Figure 1: Comparison between the proposed Algorithm 1 and the existing GNE approach in 9130079 with various parameter combinations under different parameters in Table I.
  • Figure 2: Triggering instants for Algorithm 1 with Compressor 3.

Theorems & Definitions (16)

  • Definition 1
  • Lemma 1
  • Remark 1
  • Remark 2
  • Lemma 2
  • Lemma 3
  • Lemma 4
  • Lemma 5
  • proof
  • Theorem 1
  • ...and 6 more