Event-Triggered Byzantine-Resilient Algorithm for Distributed Optimization With Sublinear Convergence
Yun-Long Li, Yan‐Wu Wang, Xiao‐Kang Liu, Jiaqi Yan, Changyun Wen · IEEE Transactions on Automatic Control · 2026
This paper focuses on Byzantine-resilient distributed optimization, aiming to minimize non-smooth strongly convex cost functions of healthy agents in adversarial environments. Therein, an event-triggered Byzantine-resilient distributed subgradient algorithm (ET-BRiDA) equipped with a new resilient filtering algorithm is proposed to address this problem. Further, a resilient output property is introduced to characterize a common property for the proposed filtering algorithm and some state-of-the-art algorithms. Under the proposed ET-BRiDA equipped with any filtering algorithm satisfying the resilient output property, the healthy agents achieve approximate consensus linearly despite Byzantine agents transmitting arbitrary incorrect messages. Moreover, their states converge sublinearly to a fixed error ball around the global minimum of the cost functions. Significantly, the analysis exposes new perspectives on the relationships among problem dimension, step-size, filter-induced weighted matrix, and convergence region. Numerical simulations and comparison studies verify the advantages of the proposed algorithm in solution accuracy and communication efficiency.