{"paper":{"title":"Accelerating Inexact HyperGradient Descent for Bilevel Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"math.OC","authors_text":"Chris Junchi Li, Haikuo Yang, Luo Luo, Michael I. Jordan","submitted_at":"2023-06-30T20:36:44Z","abstract_excerpt":"We present a method for solving general nonconvex-strongly-convex bilevel optimization problems. Our method -- the \\emph{Restarted Accelerated HyperGradient Descent} (\\texttt{RAHGD}) method -- finds an $\\epsilon$-first-order stationary point of the objective with $\\tilde{\\mathcal{O}}(\\kappa^{3.25}\\epsilon^{-1.75})$ oracle complexity, where $\\kappa$ is the condition number of the lower-level objective and $\\epsilon$ is the desired accuracy. We also propose a perturbed variant of \\texttt{RAHGD} for finding an $\\big(\\epsilon,\\mathcal{O}(\\kappa^{2.5}\\sqrt{\\epsilon}\\,)\\big)$-second-order stationary"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.00126","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/2307.00126/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"}