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Compression-based Privacy Preservation for Distributed Nash Equilibrium Seeking in Aggregative Games

Wei Huo, Xiaomeng Chen, Kemi Ding, Subhrakanti Dey, Ling Shi

TL;DR

This work addresses privacy and communication efficiency in distributed aggregative games by introducing CP-DNES, a DP-enabled DNES algorithm that leverages stochastic compression to hide information and reduce transmissions while still converging to the Nash equilibrium in mean square. By designing diminishing step sizes and employing a random quantization compressor, CP-DNES achieves $(0,\delta)$-DP with provable convergence despite non-vanishing compression errors. The authors establish theoretical results on convergence rates and DP levels, and validate them with energy-management simulations that demonstrate substantial communication savings. The approach offers a practical pathway to privacy-preserving distributed optimization in networked multi-agent systems, with potential extensions to adaptive compression and stochastic event-triggered schemes.

Abstract

This paper explores distributed aggregative games in multi-agent systems. Current methods for finding distributed Nash equilibrium require players to send original messages to their neighbors, leading to communication burden and privacy issues. To jointly address these issues, we propose an algorithm that uses stochastic compression to save communication resources and conceal information through random errors induced by compression. Our theoretical analysis shows that the algorithm guarantees convergence accuracy, even with aggressive compression errors used to protect privacy. We prove that the algorithm achieves differential privacy through a stochastic quantization scheme. Simulation results for energy consumption games support the effectiveness of our approach.

Compression-based Privacy Preservation for Distributed Nash Equilibrium Seeking in Aggregative Games

TL;DR

This work addresses privacy and communication efficiency in distributed aggregative games by introducing CP-DNES, a DP-enabled DNES algorithm that leverages stochastic compression to hide information and reduce transmissions while still converging to the Nash equilibrium in mean square. By designing diminishing step sizes and employing a random quantization compressor, CP-DNES achieves -DP with provable convergence despite non-vanishing compression errors. The authors establish theoretical results on convergence rates and DP levels, and validate them with energy-management simulations that demonstrate substantial communication savings. The approach offers a practical pathway to privacy-preserving distributed optimization in networked multi-agent systems, with potential extensions to adaptive compression and stochastic event-triggered schemes.

Abstract

This paper explores distributed aggregative games in multi-agent systems. Current methods for finding distributed Nash equilibrium require players to send original messages to their neighbors, leading to communication burden and privacy issues. To jointly address these issues, we propose an algorithm that uses stochastic compression to save communication resources and conceal information through random errors induced by compression. Our theoretical analysis shows that the algorithm guarantees convergence accuracy, even with aggressive compression errors used to protect privacy. We prove that the algorithm achieves differential privacy through a stochastic quantization scheme. Simulation results for energy consumption games support the effectiveness of our approach.
Paper Structure (16 sections, 7 theorems, 33 equations, 4 figures, 2 tables, 1 algorithm)

This paper contains 16 sections, 7 theorems, 33 equations, 4 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Statement
  3. Attacker and DP
  4. Problem Formulation
  5. Algorithm Development
  6. Convergence Analysis
  7. Differential Privacy Analysis
  8. Numerical Simulations
  9. Convergence-Communication-Privacy Trade-off
  10. Comparison with State-of-the-Art
  11. Conclusion and Future Work
  12. Useful Lemmas
  13. Proof of Lemma 1
  14. Proof of Theorem 1
  15. Proof of Corollary 1
  16. ...and 1 more sections

Key Result

Lemma 1

Suppose Assumptions assum: graph--assum: compressor hold, then $\sum_{k=0}^{\infty} \beta_{k} \mathbb{E} [\| \mathbf{y}_{k} - \mathbf{1} \bar{\mathbf{x}}_{k}\|^{2}] < \infty$ if $\sum_{k=0}^{\infty} \alpha_{k}^{2} \beta_{k} < \infty$, and $\sum_{k=0}^{\infty} \beta_{k}^{2} < \infty$.

Figures (4)

  • Figure 1: Illustration of the stochastic compressor in Definition \ref{['defn: random_quantization']}.
  • Figure 2: Comparison between conventional DNES without compression-based privacy preservation ye2017distributed and CP-DNES with different compression parameters shown in Table \ref{['tab: params']}.
  • Figure 3: Comparison between NP-DNES ye2021differentially, DSC-DNES yi2022communicationliao2023linearly, and CP-DNES: $\mathbb{C}_{3}$.
  • Figure : CP-DNES

Theorems & Definitions (24)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Remark 1
  • Remark 2
  • Lemma 1
  • proof
  • Theorem 1
  • proof
  • ...and 14 more