{"paper":{"title":"On the Condition Number Dependency in Bilevel Optimization","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["cs.AI","cs.LG"],"primary_cat":"math.OC","authors_text":"Jingzhao Zhang, Lesi Chen","submitted_at":"2025-11-27T11:03:24Z","abstract_excerpt":"Bilevel optimization minimizes an objective function, defined by an upper-level problem whose feasible region is the solution of a lower-level problem. We study the oracle complexity of finding an $\\epsilon$-stationary point with first-order methods when the upper-level problem is nonconvex, and the lower-level problem is strongly convex. Recent works (Ji et al., ICML 2021; Arbel and Mairal, ICLR 2022; Chen et al., JMLR 2025) achieve a $\\tilde{\\mathcal{O}}(\\bar \\kappa_y^4 \\epsilon^{-2})$ upper bound that is near-optimal in $\\epsilon$, which can be reduced to $\\tilde{\\mathcal{O}}(\\bar \\kappa_y^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.22331","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/2511.22331/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"}