{"paper":{"title":"Lower Bounds for Non-Convex Stochastic Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","cs.LG","math.IT","stat.ML"],"primary_cat":"math.OC","authors_text":"Blake Woodworth, Dylan J. Foster, John C. Duchi, Nathan Srebro, Yair Carmon, Yossi Arjevani","submitted_at":"2019-12-05T03:37:44Z","abstract_excerpt":"We lower bound the complexity of finding $\\epsilon$-stationary points (with gradient norm at most $\\epsilon$) using stochastic first-order methods. In a well-studied model where algorithms access smooth, potentially non-convex functions through queries to an unbiased stochastic gradient oracle with bounded variance, we prove that (in the worst case) any algorithm requires at least $\\epsilon^{-4}$ queries to find an $\\epsilon$ stationary point. The lower bound is tight, and establishes that stochastic gradient descent is minimax optimal in this model. In a more restrictive model where the noisy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.02365","kind":"arxiv","version":2},"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/1912.02365/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"}