{"paper":{"title":"Minimax Optimal Convergence of Gradient Descent in Logistic Regression via Large and Adaptive Stepsizes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Jingfeng Wu, Licong Lin, Peter L. Bartlett, Ruiqi Zhang","submitted_at":"2025-04-05T08:34:20Z","abstract_excerpt":"We study $\\textit{gradient descent}$ (GD) for logistic regression on linearly separable data with stepsizes that adapt to the current risk, scaled by a constant hyperparameter $\\eta$. We show that after at most $1/\\gamma^2$ burn-in steps, GD achieves a risk upper bounded by $\\exp(-\\Theta(\\eta))$, where $\\gamma$ is the margin of the dataset. As $\\eta$ can be arbitrarily large, GD attains an arbitrarily small risk $\\textit{immediately after the burn-in steps}$, though the risk evolution may be $\\textit{non-monotonic}$.\n  We further construct hard datasets with margin $\\gamma$, where any batch (o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.04105","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/2504.04105/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"}