{"paper":{"title":"Dual Averaging on Compactly-Supported Distributions And Application to No-Regret Learning on a Continuum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Walid Krichene","submitted_at":"2015-04-29T04:41:44Z","abstract_excerpt":"We consider an online learning problem on a continuum. A decision maker is given a compact feasible set $S$, and is faced with the following sequential problem: at iteration~$t$, the decision maker chooses a distribution $x^{(t)} \\in \\Delta(S)$, then a loss function $\\ell^{(t)} : S \\to \\mathbb{R}_+$ is revealed, and the decision maker incurs expected loss $\\langle \\ell^{(t)}, x^{(t)} \\rangle = \\mathbb{E}_{s \\sim x^{(t)}} \\ell^{(t)}(s)$. We view the problem as an online convex optimization problem on the space $\\Delta(S)$ of Lebesgue-continnuous distributions on $S$. We prove a general regret b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07720","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"}