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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1312.1530","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2013-12-05T13:00:23Z","cross_cats_sorted":[],"title_canon_sha256":"20281e4f73db807613ccbe839409913dfb2686d9b8a024cda73732e69cc70075","abstract_canon_sha256":"0fe7e4be75bbe802392423ec03b0c9ebc4fcf3ac56e5d27bc192b58e02ac5ca5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:17.388243Z","signature_b64":"JCZbqmXoYom4DseKBVhoLw5HRbW6zu6syoHuBvJbu2xhr+aBWx9fTBCynLH823hQunf1U36xRktMj/MtqNs4Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f0ded4f3f1735b3b580557ba3907a75902af25a55e67e424da993ad6a6f7645","last_reissued_at":"2026-05-18T02:48:17.387753Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:17.387753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\{1,\\dots, n\\}$. 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