Byzantine-robust distributed sparse learning for M-estimation

In a distributed computing environment, there is usually small fraction of machines that are corrupted and send arbitrary erroneous information to the master machine. This phenomenon modeled as Byzantine failure. Byzantine-robust learning has recently become an important topic in machine research. this paper, we develop Byzantine-resilient method for sparse M-estimation problem. When loss function non-smooth, it computationally costly solve penalized non-smooth optimization problem direct manner. To alleviate computational burden, construct pseudo-response variable transform original into $$\ell _1$$ -penalized least-squares problem, which much more feasible. Based on idea, communication-efficient algorithm. Theoretically, show proposed estimator obtains fast convergence rate with only constant number iterations. Furthermore, establish support recovery result, which, best our knowledge, first such result literature learning. We demonstrate effectiveness approach simulation.