Approximately Truthful Multi-Agent Optimization Using Cloud-Enforced Joint Differential Privacy

Multi-agent coordination problems often require agents to exchange state information in order to reach some collective goal, such as agreement on a final state value. In some cases, it is feasible that opportunistic agents may deceptively report false state values for their own benefit, e.g., to claim a larger portion of shared resources. Motivated by such cases, this paper presents a multi-agent coordination framework which disincentivizes opportunistic misreporting of state information. This paper focuses on multi-agent coordination problems that can be stated as nonlinear programs, with non-separable constraints coupling the agents. In this setting, an opportunistic agent may be tempted to skew the problem's constraints in its favor to reduce its local cost, and this is exactly the behavior we seek to disincentivize. The framework presented uses a primal-dual approach wherein the agents compute primal updates and a centralized cloud computer computes dual updates. All computations performed by the cloud are carried out in a way that enforces joint differential privacy, which adds noise in order to dilute any agent's influence upon the value of its cost function in the problem. We show that this dilution deters agents from intentionally misreporting their states to the cloud, and present bounds on the possible cost reduction an agent can attain through misreporting its state. This work extends our earlier work on incorporating ordinary differential privacy into multi-agent optimization, and we show that this work can be modified to provide a disincentivize for misreporting states to the cloud. Numerical results are presented to demonstrate convergence of the optimization algorithm under joint differential privacy.Comment: 17 pages, 3 figure

Privacy-Preserving Distributed Optimization via Subspace Perturbation: A General Framework

As the modern world becomes increasingly digitized and interconnected, distributed signal processing has proven to be effective in processing its large volume of data. However, a main challenge limiting the broad use of distributed signal processing techniques is the issue of privacy in handling sensitive data. To address this privacy issue, we propose a novel yet general subspace perturbation method for privacy-preserving distributed optimization, which allows each node to obtain the desired solution while protecting its private data. In particular, we show that the dual variables introduced in each distributed optimizer will not converge in a certain subspace determined by the graph topology. Additionally, the optimization variable is ensured to converge to the desired solution, because it is orthogonal to this non-convergent subspace. We therefore propose to insert noise in the non-convergent subspace through the dual variable such that the private data are protected, and the accuracy of the desired solution is completely unaffected. Moreover, the proposed method is shown to be secure under two widely-used adversary models: passive and eavesdropping. Furthermore, we consider several distributed optimizers such as ADMM and PDMM to demonstrate the general applicability of the proposed method. Finally, we test the performance through a set of applications. Numerical tests indicate that the proposed method is superior to existing methods in terms of several parameters like estimated accuracy, privacy level, communication cost and convergence rate