{"paper":{"title":"AdaGrad does not adapt to H\\\"older-smoothness for composite objectives","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"math.OC","authors_text":"Massimiliano Pontil, Matia Bojovic, Saverio Salzo","submitted_at":"2026-06-29T07:31:55Z","abstract_excerpt":"We exhibit a simple deterministic one-dimensional convex composite optimization problem for which AdaGrad scheme does not achieve the classical convergence rate $\\mathcal{O}(n^{-(1+\\nu)/2})$ associated with H\\\"older-smooth objectives. The example highlights a basic mismatch between classical AdaGrad accumulation and composite optimality. A main insight is that the gradient of the smooth term may not vanish at the optimum, causing AdaGrad to keep reducing its stepsize excessively and converge more slowly. We also discuss why alternative accumulation mechanisms based on gradient mappings or on s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29893","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/2606.29893/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"}