Resilient distributed optimization algorithm against adversary attacks

In the distributed optimization, multiple agents aim to minimize the average of all local cost functions corresponding to one decision variable. Recently, the resilient algorithms for distributed optimization against attacks have received some attention, where it is assumed that the maximum number of tolerable attacks is strictly limited by the network connectivity. To relax this assumption, in this paper, we propose a resilient distribution optimization algorithm by exploiting the trusted agents, which cannot be compromised by adversary attacks. We prove that local variables of all normal agents can converge under the proposed algorithm if the trusted agents induce the connected dominating set of the original network. Furthermore, we exploit that the final solution of normal agents will converge to the convex optima set of the weighted average of all normal agents' local functions. We also show that the amount of tolerable adversary agents is not limited by the network connectivity under the proposed algorithm. Numerical results demonstrate the effectiveness of the proposed algorithm.