Privacy-Preserving Distributed Maximum Consensus

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.