{"paper":{"title":"Decentralized Stochastic Nonconvex Optimization under the $(L_0,L_1)$-Smoothness","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.OC","authors_text":"Cheng Chen, Luo Luo, Tingkai Jia, Xue Cui","submitted_at":"2025-09-10T16:17:19Z","abstract_excerpt":"This paper focuses on the decentralized stochastic optimization problem $f(\\mathbf{x})=\\frac{1}{m}\\sum_{i=1}^m f_i(\\mathbf{x})$ over a connected network of $n$ agents, where each local function has the form of $f_i(\\mathbf{x}) = {\\mathbb E}\\left[F(\\mathbf{x};{\\boldsymbol \\xi}_i)\\right]$ which satisfies the $(L_0,L_1)$-smooth condition but possibly nonconvex and each random variable ${\\boldsymbol \\xi}_i$ follows distribution ${\\mathcal D}_i$. We propose a novel algorithm called decentralized normalized stochastic gradient descent (DNSGD), which can achieve an $\\epsilon$-stationary point at each"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.08726","kind":"arxiv","version":3},"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/2509.08726/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"}