Privacy-preserving Decentralized Optimization Based on ADMM

In this paper, we address the problem of privacypreservation in decentralized optimization, where N agents cooperatively minimize an objective function that is the sum of N strongly convex functions private to these individual agents. In most existing decentralized optimization approaches, participating agents exchange and disclose estimates explicitly, which may not be desirable when the estimates contain sensitive information of individual agents. The problem is more acute when adversaries exist which try to steal information from other participating agents. To address this issue, we propose a privacypreserving decentralized optimization approach based on ADMM and partially homomorphic cryptography. In contrast to differential privacy based approaches which use noise to cover sensitive information and are subject to a trade-off between privacy and accuracy, our approach can provide privacy without compromising the optimality of the solution. To our knowledge, this is the first time that cryptographic techniques are incorporated in a fully decentralized setting to enable privacy preservation in decentralized optimization in the absence of any third party or aggegator. To facilitate the incorporation of encryption in a fully decentralized manner, we also introduce a new ADMM which allows time-varying penalty matrices and rigorously prove its convergence. Numerical simulations confirm the effectiveness and low computational complexity of the proposed approach.