Fast Distributed Optimization over Directed Graphs under Malicious Attacks using Trust

TL;DR

This paper presents RP3, a resilient distributed optimization algorithm for directed graphs that uses trust and gradient tracking to withstand malicious attacks while ensuring fast convergence.

Contribution

Introduction of RP3, a novel algorithm that combines trust-based stochastic updates and growing constraints to achieve resilient, fast convergence in adversarial directed network settings.

Findings

RP3 achieves geometric convergence in expectation.

RP3 effectively mitigates malicious agent impact.

Numerical results confirm robustness and convergence speed.

Abstract

In this work, we introduce the Resilient Projected Push-Pull (RP3) algorithm designed for distributed optimization in multi-agent cyber-physical systems with directed communication graphs and the presence of malicious agents. Our algorithm leverages stochastic inter-agent trust values and gradient tracking to achieve geometric convergence rates in expectation even in adversarial environments. We introduce growing constraint sets to limit the impact of the malicious agents without compromising the geometric convergence rate of the algorithm. We prove that RP3 converges to the nominal optimal solution almost surely and in the $r$-th mean for any $r\geq 1$, provided the step sizes are sufficiently small and the constraint sets are appropriately chosen. We validate our approach with numerical studies on average consensus and multi-robot target tracking problems, demonstrating that RP3 effectively mitigates the impact of malicious agents and achieves the desired geometric convergence.