{"paper":{"title":"Auto-Conditioned Frank-Wolfe Algorithms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Frank-Wolfe methods converge with local Lipschitz estimates alone","cross_cats":[],"primary_cat":"math.OC","authors_text":"Khanh-Hung Giang-Tran, Nam Ho-Nguyen, Soroosh Shafiee","submitted_at":"2026-05-15T01:12:32Z","abstract_excerpt":"Frank-Wolfe methods are projection-free algorithms for constrained optimization whose practical performance often depends critically on the choice of step size. Classical closed-loop step-size rules typically require prior knowledge of a global smoothness constant, while line-search variants avoid this requirement at the cost of additional function evaluations and implementation overhead. In this paper, we develop a fully auto-conditioned framework for Frank-Wolfe-type methods. The framework replaces the global Lipschitz constant in closed-loop step sizes with a local Lipschitz estimator compu"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We develop a fully auto-conditioned framework for Frank-Wolfe-type methods that replaces the global Lipschitz constant in closed-loop step sizes with a local Lipschitz estimator computed from first-order information along the iterates, establishing convergence to stationary points in the nonconvex setting and recovering standard sublinear convergence guarantees in the convex setting without requiring prior knowledge of a global smoothness constant.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The local Lipschitz estimator computed from first-order information along the iterates is accurate enough to serve as a drop-in replacement for the global smoothness constant while preserving the convergence analysis for the general class of methods including standard Frank-Wolfe, Matching Pursuit, pairwise Frank-Wolfe, and away-step Frank-Wolfe.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Auto-conditioned Frank-Wolfe methods use local Lipschitz estimators from first-order information to achieve convergence guarantees in convex and nonconvex settings without prior global smoothness knowledge.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Frank-Wolfe methods converge with local Lipschitz estimates alone","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"59f08c421274a0462cca023e92935f5b94cbd8e5b515308e8051c53598c5b0c5"},"source":{"id":"2605.15512","kind":"arxiv","version":1},"verdict":{"id":"69114878-b05a-4e8b-8c5d-48c2ae917e6c","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T15:29:18.700844Z","strongest_claim":"We develop a fully auto-conditioned framework for Frank-Wolfe-type methods that replaces the global Lipschitz constant in closed-loop step sizes with a local Lipschitz estimator computed from first-order information along the iterates, establishing convergence to stationary points in the nonconvex setting and recovering standard sublinear convergence guarantees in the convex setting without requiring prior knowledge of a global smoothness constant.","one_line_summary":"Auto-conditioned Frank-Wolfe methods use local Lipschitz estimators from first-order information to achieve convergence guarantees in convex and nonconvex settings without prior global smoothness knowledge.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The local Lipschitz estimator computed from first-order information along the iterates is accurate enough to serve as a drop-in replacement for the global smoothness constant while preserving the convergence analysis for the general class of methods including standard Frank-Wolfe, Matching Pursuit, pairwise Frank-Wolfe, and away-step Frank-Wolfe.","pith_extraction_headline":"Frank-Wolfe methods converge with local Lipschitz estimates alone"},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15512/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T16:01:17.912268Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T15:40:36.682832Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"cited_work_retraction","ran_at":"2026-05-19T14:51:54.960637Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T14:21:54.055095Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"shingle_duplication","ran_at":"2026-05-19T13:49:41.848252Z","status":"skipped","version":"0.1.0","findings_count":0},{"name":"citation_quote_validity","ran_at":"2026-05-19T13:49:41.387156Z","status":"skipped","version":"0.1.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T13:33:22.634630Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"30a0fcc2951c5874d155ffc2704696e7a70a1c961d78229f3de7752d5aeaea7b"},"references":{"count":63,"sample":[{"doi":"","year":2023,"title":"A. 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