{"paper":{"title":"Bandit Online Optimization Over the Permutahedron","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Eiji Takimoto, Kohei Hatano, Nir Ailon","submitted_at":"2013-12-05T13:00:23Z","abstract_excerpt":"The permutahedron is the convex polytope with vertex set consisting of the vectors $(\\pi(1),\\dots, \\pi(n))$ for all permutations (bijections) $\\pi$ over $\\{1,\\dots, n\\}$. We study a bandit game in which, at each step $t$, an adversary chooses a hidden weight weight vector $s_t$, a player chooses a vertex $\\pi_t$ of the permutahedron and suffers an observed loss of $\\sum_{i=1}^n \\pi(i) s_t(i)$.\n  A previous algorithm CombBand of Cesa-Bianchi et al (2009) guarantees a regret of $O(n\\sqrt{T \\log n})$ for a time horizon of $T$. Unfortunately, CombBand requires at each step an $n$-by-$n$ matrix per"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1530","kind":"arxiv","version":2},"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"}