Byzantine-robust distributed one-step estimation

• DOI: 10.48550/arxiv.2307.07767
• Publication Date: 2023-01-01
• Authors: Chuhan Wang; Xuehu Zhu; Li Zhu
• Keywords: Delta method; Hessian matrix; Robustness

This paper proposes a Robust One-Step Estimator(ROSE) to solve the Byzantine failure problem in distributed M-estimation when moderate fraction of node machines experience failures. To define ROSE, algorithms use robust Variance Reduced Median Of Local(VRMOL) estimator determine initial parameter value for iteration, and communicate between central processor Newton-Raphson iteration procedure derive VRMOL gradient, Hessian matrix so as obtain final estimator. ROSE has higher asymptotic relative efficiency than general median estimators without increasing order computational complexity. Moreover, this can also cope with problems involving anomalous or missing samples on processor. We prove normality dimension p diverges sample size goes infinity, under weaker assumptions, convergence rate. Numerical simulations real data application are conducted evidence effectiveness robustness ROSE.