{"paper":{"title":"Adaptive Open-Loop Step-Sizes for Accelerated Convergence Rates of the Frank-Wolfe Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Elias Wirth, Javier Pe\\~na, Sebastian Pokutta","submitted_at":"2025-05-15T01:09:03Z","abstract_excerpt":"Recent work has shown that in certain settings, the Frank-Wolfe algorithm (FW) with open-loop step-sizes $\\eta_t = \\frac{\\ell}{t+\\ell}$ for a fixed parameter $\\ell \\in \\mathbb{N},\\, \\ell \\geq 2$, attains a convergence rate faster than the traditional $O(t^{-1})$ rate. In particular, when a strong growth property holds, the convergence rate attainable with open-loop step-sizes $\\eta_t = \\frac{\\ell}{t+\\ell}$ is $O(t^{-\\ell})$. In this setting there is no single value of the parameter $\\ell$ that prevails as superior. This paper shows that FW with log-adaptive open-loop step-sizes $\\eta_t = \\frac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.09886","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/2505.09886/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"}