Resilient Primal–Dual Optimization Algorithms for Distributed Resource Allocation

Abstract

Distributed algorithms for multi-agent resource allocation can provide\nprivacy and scalability over centralized algorithms in many cyber-physical\nsystems. However, the distributed nature of these algorithms can render these\nsystems vulnerable to man-in-the-middle attacks that can lead to\nnon-convergence and infeasibility of resource allocation schemes. In this\npaper, we propose attack-resilient distributed algorithms based on primal-dual\noptimization when Byzantine attackers are present in the system. In particular,\nwe design attack-resilient primal-dual algorithms for static and dynamic\nimpersonation attacks by means of robust statistics. For static impersonation\nattacks, we formulate a robustified optimization model and show that our\nalgorithm guarantees convergence to a neighborhood of the optimal solution of\nthe robustified problem. On the other hand, a robust optimization model is not\nrequired for the dynamic impersonation attack scenario and we are able to\ndesign an algorithm that is shown to converge to a near-optimal solution of the\noriginal problem. We analyze the performances of our algorithms through both\ntheoretical and computational studies.\n