# Byzantine-Robust Distributed Sparse Learning Revisited

arXiv: https://arxiv.org/abs/2605.13283 · HTML: https://mlsanity.com/paper/2605.13283/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 27 references that are in the map.
- First posted on arXiv 13 May 2026.

## Builds on (most cited first, 9 of 9)

- [Byzantine-Robust Distributed Learning: Towards Optimal Statistical Rates](https://mlsanity.com/paper/1803.01498/) (2018)
- [Communication Efficient Distributed Optimization using an Approximate Newton-type Method](https://mlsanity.com/paper/1312.7853/) (2013)
- [Efficient Distributed Learning with Sparsity](https://mlsanity.com/paper/1605.07991/) (2016)
- [Communication-Efficient Accurate Statistical Estimation](https://mlsanity.com/paper/1906.04870/) (2019)
- [Smoothed Quantile Regression with Large-Scale Inference](https://mlsanity.com/paper/2012.05187/) (2020)
- [A Huber Loss Minimization Approach to Byzantine Robust Federated Learning](https://mlsanity.com/paper/2308.12581/) (2023)
- [Variance Reduced Median-of-Means Estimator for Byzantine-Robust Distributed Inference](https://mlsanity.com/paper/2103.02860/) (2021)
- [Sparse Quantile Huber Regression for Efficient and Robust Estimation](https://mlsanity.com/paper/1402.4624/) (2014)
- [Distributed Adaptive Huber Regression](https://mlsanity.com/paper/2107.02726/) (2021)

## Abstract (arXiv)

We revisit Byzantine robust distributed estimation for high-dimensional sparse linear models. By combining local ℓ1-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.