{"paper":{"title":"Artificial Constraints and Lipschitz Hints for Unconstrained Online Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.OC"],"primary_cat":"stat.ML","authors_text":"Ashok Cutkosky","submitted_at":"2019-02-24T20:30:59Z","abstract_excerpt":"We provide algorithms that guarantee regret $R_T(u)\\le \\tilde O(G\\|u\\|^3 + G(\\|u\\|+1)\\sqrt{T})$ or $R_T(u)\\le \\tilde O(G\\|u\\|^3T^{1/3} + GT^{1/3}+ G\\|u\\|\\sqrt{T})$ for online convex optimization with $G$-Lipschitz losses for any comparison point $u$ without prior knowledge of either $G$ or $\\|u\\|$. Previous algorithms dispense with the $O(\\|u\\|^3)$ term at the expense of knowledge of one or both of these parameters, while a lower bound shows that some additional penalty term over $G\\|u\\|\\sqrt{T}$ is necessary. Previous penalties were exponential while our bounds are polynomial in all quantitie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.09013","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":""},"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"}