User-preference-aware Private-preserving Average Consensus

Privacy-preserving average consensus is important for multi-agent systems and has been extensively studied. Considering the more practical scenario that different users may have different privacy preferences, there exists a tradeoff between the convergence time and the data privacy protection. In this paper, we design the added noises with the optimal variances considering the heterogeneous user preferences. We develop a novel definition on the convergence time for ensuring (α, γ)- accuracy, which depicts how fast the consensus protocol can converge to the average with a bounded deviation, α, with a probability no smaller than 1 - γ. We obtain the analytical expression for the upper bound of the convergence time. We design the utility of each agent which is inversely proportional to the privacy preference, such that some user may prefer a lower privacy for a higher utility. With the introduction of the reward- incentive mechanism, we then formulate optimization problems to optimize the distribution and the variance of the added noises. Simulations were conducted to verify the analysis.