{"paper":{"title":"On the Complexity of Decentralized Smooth Nonconvex Finite-Sum Optimization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.OC","authors_text":"Haishan Ye, Lesi Chen, Luo Luo, Yunyan Bai, Yuxing Liu","submitted_at":"2022-10-25T11:37:11Z","abstract_excerpt":"We study the decentralized optimization problem $\\min_{{\\bf x}\\in{\\mathbb R}^d} f({\\bf x})\\triangleq \\frac{1}{m}\\sum_{i=1}^m f_i({\\bf x})$, where the local function on the $i$-th agent has the form of $f_i({\\bf x})\\triangleq \\frac{1}{n}\\sum_{j=1}^n f_{i,j}({\\bf x})$ and every individual $f_{i,j}$ is smooth but possibly nonconvex. We propose a stochastic algorithm called DEcentralized probAbilistic Recursive gradiEnt deScenT (DEAREST) method, which achieves an $\\epsilon$-stationary point at each agent with the communication rounds of $\\tilde{\\mathcal O}(L\\epsilon^{-2}/\\sqrt{\\gamma}\\,)$, the com"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.13931","kind":"arxiv","version":4},"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/2210.13931/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"}