We propose a privacy-preserving distributed maximum consensus algorithm where the local state of the agents and identity of the maximum state owner is kept private from adversaries. To that end, we reformulate the maximum consensus problem over a distributed network as a linear program. This optimization problem is solved in a distributed manner using the alternating direction method of multipliers (ADMM) and perturbing the primal update step with Gaussian noise. We define the privacy of an agent as the estimation error of its local state at the adversary and obtain theoretical bounds on the privacy loss for the proposed method. Further, we prove that the proposed algorithm converges to the maximum value at all agents. In addition to the analytical results, we illustrate the convergence speed and privacy-accuracy trade-off through numerical simulations.

中文翻译：

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隐私保护分布式最大共识

我们提出了一种保护隐私的分布式最大共识算法，其中代理的本地状态和最大状态所有者的身份对对手保密。为此，我们将分布式网络上的最大共识问题重新表述为线性程序。该优化问题使用乘法器交替方向法 (ADMM) 以分布式方式解决，并使用高斯噪声扰动原始更新步骤。我们将代理的隐私定义为对手对其本地状态的估计误差，并获得所提出方法的隐私损失的理论界限。此外，我们证明了所提出的算法收敛到所有代理的最大值。除了分析结果，