Byzantine-Robust Sparse Regression with Missing Covariates

We study distributed sparse linear regression with missing covariates and Byzantine workers. Correcting for missing observations can make the regression loss nonconvex, while Byzantine reports can distort gradient updates and impair estimation. A communication-efficient method is proposed that combines robust gradient aggregation with folded-concave regularization. Under appropriate regularity conditions, after $t$ communication rounds the estimation error is bounded by a transient component determined by the initial error and decaying geometrically with $t$, plus a residual component reflecting finite-sample variability and Byzantine contamination. Simulations and two real-data examples evaluate estimation accuracy, variable selection, and communication costs.