{"paper":{"title":"Stochastic continuum armed bandit problem of few linear parameters in high dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.OC"],"primary_cat":"stat.ML","authors_text":"Bernd G\\\"artner, Hemant Tyagi, Sebastian Stich","submitted_at":"2013-12-01T15:16:25Z","abstract_excerpt":"We consider a stochastic continuum armed bandit problem where the arms are indexed by the $\\ell_2$ ball $B_{d}(1+\\nu)$ of radius $1+\\nu$ in $\\mathbb{R}^d$. The reward functions $r :B_{d}(1+\\nu) \\rightarrow \\mathbb{R}$ are considered to intrinsically depend on $k \\ll d$ unknown linear parameters so that $r(\\mathbf{x}) = g(\\mathbf{A} \\mathbf{x})$ where $\\mathbf{A}$ is a full rank $k \\times d$ matrix. Assuming the mean reward function to be smooth we make use of results from low-rank matrix recovery literature and derive an efficient randomized algorithm which achieves a regret bound of $O(C(k,d)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0232","kind":"arxiv","version":4},"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"}