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

TL;DR

This paper introduces a novel privacy-preserving average consensus algorithm for multi-agent systems on unbalanced directed networks, embedding randomness and auxiliary parameters to ensure privacy without sacrificing convergence speed.

Contribution

The paper presents a new algorithm that guarantees exact average consensus while preserving privacy against various attacks, differing from differential privacy approaches.

Findings

Converges linearly to the exact average consensus value.

Guarantees privacy against honest-but-curious and eavesdropping attacks.

Validated by numerical experiments.

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.