On Distributed Optimization in the Presence of Malicious Agents

In this paper, we consider an unconstrained distributed optimization problem over a network of agents, in which some agents are adversarial. We solve the problem via gradient-based distributed optimization algorithm and characterize the effect of the adversarial agents on the convergence of the algorithm to the optimal solution. The attack model considered is such that agents locally perturb their iterates before broadcasting it to neighbors; and we analyze the case in which the adversarial agents cooperate in perturbing their estimates and the case where each adversarial agent acts independently. Based on the attack model adopted in the paper, we show that the solution converges to the neighborhood of the optimal solution and depends on the magnitude of the attack (perturbation) term. The analyses presented establishes conditions under which the malicious agents have enough information to obstruct convergence to the optimal solution by the non-adversarial agents.