Resilient Distributed Optimization Algorithm With Fixed Step Size Against Malicious Attacks

Solving distributed optimization problems relies on information exchange between nodes in multi-agent networks. In an unreliable network environment with malicious attacks, compromised nodes deliberately disseminate falsified data to disrupt the optimization process. The security and robustness of the multi-agent system can be improved by designing the fault-tolerant mechanism (FTM) and the resilient distributed optimization (RDO) algorithm. This paper introduces a new fault-tolerant mechanism based on K-Medoids clustering (M-FTM) to address the challenges posed by malicious attacks. Compared with the existing $ F$-local filtering mechanism, M-FTM reduces the network connectivity requirement from $ (2F +1)$-robust to $ (F +1)$-robust, where $ F$ is the number of malicious nodes in the network. This article addresses high-dimensional optimization problems, for which the resilient DIGing algorithm and the resilient Push-DIGing algorithm with fixed step size are proposed. The effectiveness of the algorithms is verified through consensus and convergence analysis. Numerical experiments show that the proposed algorithms can effectively resist malicious attacks. Additionally, M-FTM not only doubles the runtime efficiency of algorithm but also enables its operation under low network connectivity conditions.