{"paper":{"title":"Byzantine-Robust Distributed Sparse Learning Revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Local l1-regularized robust estimators plus server-side robust aggregation deliver non-asymptotic guarantees and near-optimal rates for Byzantine-robust distributed sparse learning.","cross_cats":["math.ST","stat.TH"],"primary_cat":"cs.LG","authors_text":"Kangqiang Li, Lixin Zhang, Yuxuan Wang","submitted_at":"2026-05-13T10:00:23Z","abstract_excerpt":"We revisit Byzantine robust distributed estimation for high-dimensional sparse linear models. By combining local $\\ell_1$-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."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"the resulting estimators yield non-asymptotic guarantees and attain near-optimal statistical rates under mild conditions, while remaining communication-efficient","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"mild conditions on the data distribution, sparsity level, and fraction of Byzantine machines (standard but unspecified in abstract; typically requires bounded moments and Byzantine fraction below 1/2)","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Local L1-regularized robust estimators plus server-side robust aggregation achieve near-optimal rates for high-dimensional sparse learning under Byzantine attacks.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Local l1-regularized robust estimators plus server-side robust aggregation deliver non-asymptotic guarantees and near-optimal rates for Byzantine-robust distributed sparse learning.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"931a1cd313433b232c29a5ac9441240578e4027418349fe94a9290a498d839bd"},"source":{"id":"2605.13283","kind":"arxiv","version":1},"verdict":{"id":"ee5a5ed2-8cc1-4210-a80e-8148a0fb3a90","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T19:37:19.514915Z","strongest_claim":"the resulting estimators yield non-asymptotic guarantees and attain near-optimal statistical rates under mild conditions, while remaining communication-efficient","one_line_summary":"Local L1-regularized robust estimators plus server-side robust aggregation achieve near-optimal rates for high-dimensional sparse learning under Byzantine attacks.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"mild conditions on the data distribution, sparsity level, and fraction of Byzantine machines (standard but unspecified in abstract; typically requires bounded moments and Byzantine fraction below 1/2)","pith_extraction_headline":"Local l1-regularized robust estimators plus server-side robust aggregation deliver non-asymptotic guarantees and near-optimal rates for Byzantine-robust distributed sparse learning."},"references":{"count":16,"sample":[{"doi":"","year":null,"title":"Sparse Quantile Huber Regression for Efficient and Robust Estimation","work_id":"2ca89efa-7258-429d-a5e8-e169cf94253c","ref_index":1,"cited_arxiv_id":"1402.4624","is_internal_anchor":true},{"doi":"10.1214/17-aos1587","year":2011,"title":"Distributed testing and estimation under sparse high dimensional models. Ann. Statist. 46, 1352–1382. doi:10.1214/17-AOS1587. Belloni,A.,Chernozhukov,V.,2011.𝓁 1-penalizedquantileregressioninhigh-dime","work_id":"d901821a-9e8a-4dc4-a53c-b106bb5d8e53","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2021,"title":"2023 , journal =","work_id":"cedbb8cd-4355-4661-9d7a-1d12a91d0dd9","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1111/rssb.12166","year":null,"title":"Estimation of high dimensional mean regression in the absence of symmetry and light tail assumptions. J. R. Stat. Soc. B: Stat. Methodol. 79, 247–265. doi:10.1111/rssb.12166. Fan, J., Liu, H., Sun, Q.","work_id":"76326722-d8c8-4407-a4e1-61becdbeb9d6","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1214/17-aos1568","year":null,"title":"I-lamm for sparse learning: Simultaneous control of algorithmic complexity and statistical error. Ann. Statist. 46, 814–841. doi:10.1214/17-AOS1568. He, X., Pan, X., Tan, K.M., Zhou, W.X.,","work_id":"c546aea9-8b24-49dd-8df0-3ad21ab0c166","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":16,"snapshot_sha256":"397490c10791ec916fb5731af52ad99796657a8ad60bd1c7bfd66f49f791cf92","internal_anchors":1},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}