Resilient Online Distributed Optimization Algorithm against Byzantine Attacks

Abstract

This paper presents a resilient online distributed optimization algorithm against Byzantine attacks. Each agent exchanges local information with neighbors on an unbalanced digraph with the row-stochastic matrix. Firstly, the gradient scaling technique based on consistency estimation is used to learn the left vector of the adjacency matrix asymptotically to overcome the imbalance of gradient weight caused by the row-stochastic matrix and improve the convergence speed and accuracy of the algorithm. Secondly, to effectively solve the problem of node consistency and optimality caused by Byzantine attacks, this paper uses the boundedness of the projection operator to limit state deviation between different nodes and extends the existing offline distributed optimization algorithm against Byzantine attacks to the online form, and regret bounds are derived for each node. Finally, the effectiveness and superiority of the proposed method are demonstrated by the comparison of numerical simulation. The results show that the proposed algorithm against Byzantine attacks extends offline form to the online form, and optimizes its accuracy and convergence speed.