Byzantine-Robust Distributed Sparse Learning Revisited

We revisit Byzantine robust distributed estimation for high-dimensional sparse linear models. By combining local ${\mathrm{\ell }}_1$-regularized robust estimation with robust aggregation at the server, the framework applies to pseudo-Huber regression, quantile regression, and sparse SVM. We show that the resulting estimators yield non-asymptotic guarantees and attain near-optimal statistical rates under mild conditions, while remaining communication-efficient. Simulations confirm strong robustness in estimation, support recovery and classification accuracy under various Byzantine attacks.