Resilient consensus for multi-agent systems subject to differential privacy requirements

TL;DR

This paper introduces a modified consensus algorithm for multi-agent systems that ensures fault tolerance and differential privacy of initial conditions, even in directed networks with adversarial agents.

Contribution

It develops the DP-MSR algorithm, combining fault-tolerance with differential privacy guarantees, and characterizes its correctness, accuracy, and privacy properties.

Findings

The algorithm achieves consensus despite up to f faulty agents in $(2f+1)$-robust networks.

It guarantees differential privacy of initial conditions under certain network degree conditions.

Simulations validate the theoretical results.

Abstract

We consider multi-agent systems interacting over directed network topologies where a subset of agents is adversary/faulty and where the non-faulty agents have the goal of reaching consensus, while fulfilling a differential privacy requirement on their initial conditions. To address this problem, we develop an update law for the non-faulty agents. Specifically, we propose a modification of the so-called Mean-Subsequence-Reduced (MSR) algorithm, the Differentially Private MSR (DP-MSR) algorithm, and characterize three important properties of the algorithm: correctness, accuracy and differential privacy. We show that if the network topology is $(2f +1)$-robust, then the algorithm allows the non-faulty agents to reach consensus despite the presence of up to $f$ faulty agents and we characterize the accuracy of the algorithm. Furthermore, we also show in two important cases that our distributed algorithm can be tuned to guarantees differential privacy of the initial conditions and the differential privacy requirement is related to the maximum network degree. The results are illustrated via simulations.