{"paper":{"title":"Optimal Complexity in Byzantine-Robust Distributed Stochastic Optimization with Data Heterogeneity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.OC","authors_text":"Jie Peng, Kun Yuan, Qiankun Shi, Qing Ling, Xiao Wang","submitted_at":"2025-03-20T16:56:06Z","abstract_excerpt":"In this paper, we establish tight lower bounds for Byzantine-robust distributed first-order stochastic optimization methods in both strongly convex and non-convex stochastic optimization. We reveal that when the distributed nodes have heterogeneous data, the convergence error comprises two components: a non-vanishing Byzantine error and a vanishing optimization error. We establish the lower bounds on the Byzantine error and on the minimum number of queries to a stochastic gradient oracle required to achieve an arbitrarily small optimization error. Nevertheless, we identify significant discrepa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.16337","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.16337/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"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"}