Byzantine-robust Distributed One-step Estimation

This paper proposes a Robust One-Step Estimator (ROSE) with one round of iteration to solve the Byzantine failure problem in distributed M-estimation when a moderate fraction of node machines experience Byzantine failures. The defined estimator has higher asymptotic relative efficiency than general median estimators without increasing the order of computational complexity. It can also cope with the problems involving anomalous or missing samples on the central processor. We prove the asymptotic normality when the dimension p of parameter vector diverges as the sample size goes to infinity, and under mild assumptions, derive the convergence rate. Numerical simulations and a real data application are conducted to evidence its effectiveness and robustness.