Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Dynamics-Based Algorithm-Level Privacy Preservation for Push-Sum Average Consensus

Huqiang Cheng, Mengying Xie, Xiaowei Yang, Qingguo Lü, Huaqing Li

TL;DR

This work tackles privacy in distributed average consensus on unbalanced directed networks. It introduces a dynamics-based, two-stage privacy-preserving push-sum that randomizes initial mixing weights and uses a public auxiliary parameter to mask early updates, while preserving a linear convergence to the exact average $\bar{x}^0$ with rate $\rho=(1-\eta^{N-1})^{1/(N-1)}$. The authors formalize privacy notions against honest-but-curious and eavesdropping attacks, prove that privacy can be maintained without sacrificing accuracy, and extend the framework to vector states. Numerical experiments on small and large directed graphs validate both the convergence properties and privacy guarantees, and comparisons with differential privacy baselines show this approach achieves exact consensus where others do not. The proposed method is practical for resource-limited networks and offers a solid foundation for privacy-preserving distributed optimization in directed settings.

Abstract

In the intricate dance of multi-agent systems, achieving average consensus is not just vital--it is the backbone of their functionality. In conventional average consensus algorithms, all agents reach an agreement by individual calculations and sharing information with their respective neighbors. Nevertheless, the information interactions that occur in the communication network may make sensitive information be revealed. In this paper, we develop a new privacy-preserving average consensus method on unbalanced directed networks. Specifically, we ensure privacy preservation by carefully embedding randomness in mixing weights to confuse communications and introducing an extra auxiliary parameter to mask the state-updated rule in several initial iterations. In parallel, we exploit the intrinsic robustness of consensus dynamics to guarantee that the average consensus is precisely achieved. Theoretical results demonstrate that the designed algorithms can converge linearly to the exact average consensus value and can guarantee privacy preservation of agents against both honest-but-curious and eavesdropping attacks. The designed algorithms are fundamentally different compared to differential privacy based algorithms that enable privacy preservation via sacrificing consensus performance. Finally, numerical experiments validate the correctness of the theoretical findings.

Dynamics-Based Algorithm-Level Privacy Preservation for Push-Sum Average Consensus

TL;DR

This work tackles privacy in distributed average consensus on unbalanced directed networks. It introduces a dynamics-based, two-stage privacy-preserving push-sum that randomizes initial mixing weights and uses a public auxiliary parameter to mask early updates, while preserving a linear convergence to the exact average with rate . The authors formalize privacy notions against honest-but-curious and eavesdropping attacks, prove that privacy can be maintained without sacrificing accuracy, and extend the framework to vector states. Numerical experiments on small and large directed graphs validate both the convergence properties and privacy guarantees, and comparisons with differential privacy baselines show this approach achieves exact consensus where others do not. The proposed method is practical for resource-limited networks and offers a solid foundation for privacy-preserving distributed optimization in directed settings.

Abstract

In the intricate dance of multi-agent systems, achieving average consensus is not just vital--it is the backbone of their functionality. In conventional average consensus algorithms, all agents reach an agreement by individual calculations and sharing information with their respective neighbors. Nevertheless, the information interactions that occur in the communication network may make sensitive information be revealed. In this paper, we develop a new privacy-preserving average consensus method on unbalanced directed networks. Specifically, we ensure privacy preservation by carefully embedding randomness in mixing weights to confuse communications and introducing an extra auxiliary parameter to mask the state-updated rule in several initial iterations. In parallel, we exploit the intrinsic robustness of consensus dynamics to guarantee that the average consensus is precisely achieved. Theoretical results demonstrate that the designed algorithms can converge linearly to the exact average consensus value and can guarantee privacy preservation of agents against both honest-but-curious and eavesdropping attacks. The designed algorithms are fundamentally different compared to differential privacy based algorithms that enable privacy preservation via sacrificing consensus performance. Finally, numerical experiments validate the correctness of the theoretical findings.
Paper Structure (20 sections, 6 theorems, 61 equations, 6 figures, 1 table, 4 algorithms)

This paper contains 20 sections, 6 theorems, 61 equations, 6 figures, 1 table, 4 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Main Contributions
  4. Preliminaries
  5. Graph Theory
  6. Conventional Push-Sum Method
  7. Privacy Concern
  8. Performance Metric
  9. Privacy-Preserving Push-Sum Algorithm
  10. Convergence Analysis
  11. Privacy Analysis
  12. Performance Against Honest-but-curious Attacks
  13. Performance Against Eavesdropping Attacks
  14. Experiments Validation
  15. Consensus Performance
  16. ...and 5 more sections

Key Result

Theorem 1

Let $\{ ( z_i( k ) ) _{i=1}^{N} \} _{k\in \mathbb{N}}$ be the sequence generated by Algorithm alg:2, and the network $\mathcal{G}$ satisfies Assumption A1. Then, it holds, for all $k\in \mathbb{N}$, where $\rho =( 1-\eta ^{N-1} ) ^{\frac{1}{N-1}}$, and $c$ is a constant given as where $c_1=2\sqrt{N}c_0\lVert \mathbf{x}( K+1 ) \rVert _1\eta ^{-N}\rho ^{-K-2}$, $c_2=2\sqrt{N}\eta ^{-N}-( N-1 ) /\s

Figures (6)

  • Figure 1: Dynamics-based protocol: A brief computation process from the view of agent $i$ over a simple $3$-agent digraph.
  • Figure 2: Communication networks. A simple directed network $\mathcal{G}_1$ with $5$ agents and a large-scale directed network $\mathcal{G}_2$ consisting of $1000$ agents.
  • Figure 3: Consensus performance. (a)-(b) The trajectories of states $\{z_i( k )\}$ and the evolutions of $e( k )$ of Algorithm 2; (c)-(d) The trajectories of states $\{\mathbf{z}_i( k )\}$ and the evolutions of $e( k )$ of Algorithm 3.
  • Figure 4: Performance of the other works. (a)-(c) The trajectories of all states $\{x_i( k )\}$ in Huang2012, Mo2017, Manitara2013 in order.
  • Figure 5: Performance of the proposed algorithm over different works. (a) The effect of out-degrees on consensus rate; (b) The effect of in-degrees on consensus rate; (c) The evolutions of $e( k )$ over the large-scale network $\mathcal{G}_2$.
  • ...and 1 more figures

Theorems & Definitions (24)

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