Privacy preservation for distributed optimization in multiagent systems has been widely concerned in recent years. In this article, the accumulated noise privacy-preserving alternating direction method of multipliers (ANPPM) algorithm is proposed to preserve the private information of each agent. The masked states of each agent are sent to its neighbors with a designed noise-adding mechanism, and an accumulated term is introduced to confuse the gradients at each iteration. With ANPPM, all the agents can achieve privacy preservation for the information of real states and subgradients. Moreover, the states of all the agents can be guaranteed to converge to the optimal solution. The convergence rate of O(1/k)O(1/k) is consistent with standard ADMM, hence no adverse effect is induced by the privacy-preserving mechanism. Numerical results are provided to validate the effectiveness of the proposed ANPPM algorithm.

中文翻译：

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ADMM 中累积噪声的分布式隐私保护优化


多智能体系统中分布式优化的隐私保护近年来受到广泛关注。本文提出了累积噪声隐私保护乘子交替方向法（ANPPM）算法来保护每个智能体的隐私信息。每个智能体的屏蔽状态通过设计的噪声添加机制发送到其邻居，并引入累积项来混淆每次迭代的梯度。通过ANPPM，所有智能体都可以实现真实状态和次梯度信息的隐私保护。而且，可以保证所有智能体的状态收敛到最优解。 O(1/k)O(1/k)的收敛速度与标准ADMM一致，因此隐私保护机制不会产生不利影响。提供数值结果来验证所提出的 ANPPM 算法的有效性。