{"paper":{"title":"Fully Implicit Online Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Chaobing Song, Han Liu, Ji Liu, Tong Zhang, Yong Jiang","submitted_at":"2018-09-25T07:16:17Z","abstract_excerpt":"Regularized online learning is widely used in machine learning applications. In online learning, performing exact minimization ($i.e.,$ implicit update) is known to be beneficial to the numerical stability and structure of solution. In this paper we study a class of regularized online algorithms without linearizing the loss function or the regularizer, which we call \\emph{fully implicit online learning} (FIOL). We show that for arbitrary Bregman divergence, FIOL has the $O(\\sqrt{T})$ regret for general convex setting and $O(\\log T)$ regret for strongly convex setting, and the regret has an one"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09350","kind":"arxiv","version":3},"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"}