{"paper":{"title":"Harnessing Unimodality in Semiparametric Contextual Pricing via Oracle Price Map Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"In semiparametric contextual pricing, a scalar-index pilot reduces the problem to learning a one-dimensional smooth oracle price map whose nonparametric cost is minimax sharp.","cross_cats":["cs.LG","math.OC"],"primary_cat":"stat.ML","authors_text":"Jinchi Lv, Xiaocong Xu, Yingying Fan, Yuxuan Han, Zhengyuan Zhou","submitted_at":"2026-05-14T20:53:23Z","abstract_excerpt":"We study contextual dynamic pricing in a semiparametric scalar-index valuation model where the latent value is $v_t=\\mu_\\ast(\\mathsf c_t)+\\xi_t$, with an unknown utility map $\\mu_\\ast$ and an unknown additive noise distribution. The key decision object is the one-dimensional oracle price map $u\\mapsto p^\\ast(u)$ induced by the scalar index $u=\\mu_\\ast(\\mathsf c)$ and the noise tail. Under the $\\beta$-H\\\"older smoothness of the tail function for $\\beta\\geq 2$ and a revenue-geometry condition that gives a unique, stable, interior maximizer, this oracle map is itself $(\\beta-1)$-smooth. We exploi"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The resulting policy achieves regret Õ(T^{(2β-1)/(4β-3)} + √(dT)). For fixed d, we establish a matching lower bound in the horizon dependence, unveiling that the nonparametric oracle-map learning term is minimax sharp.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The revenue-geometry condition that gives a unique, stable, interior maximizer of the expected revenue function for each scalar index u (invoked to guarantee that the oracle price map is well-defined and (β-1)-smooth).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"ORBIT learns the (β-1)-smooth oracle price map via local polynomial approximation and bandit convex optimization in a semiparametric contextual pricing model, achieving regret Õ(T^{(2β-1)/(4β-3)} + √(dT)) with a matching lower bound for fixed d.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"In semiparametric contextual pricing, a scalar-index pilot reduces the problem to learning a one-dimensional smooth oracle price map whose nonparametric cost is minimax sharp.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"d35d7ce6e354ce026ce1c05fbad854bd071ce169fd87e6b014b4fb75eec128ab"},"source":{"id":"2605.15411","kind":"arxiv","version":1},"verdict":{"id":"6b10b5c9-841a-4362-bd21-12eb064469a2","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T15:15:31.851902Z","strongest_claim":"The resulting policy achieves regret Õ(T^{(2β-1)/(4β-3)} + √(dT)). For fixed d, we establish a matching lower bound in the horizon dependence, unveiling that the nonparametric oracle-map learning term is minimax sharp.","one_line_summary":"ORBIT learns the (β-1)-smooth oracle price map via local polynomial approximation and bandit convex optimization in a semiparametric contextual pricing model, achieving regret Õ(T^{(2β-1)/(4β-3)} + √(dT)) with a matching lower bound for fixed d.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The revenue-geometry condition that gives a unique, stable, interior maximizer of the expected revenue function for each scalar index u (invoked to guarantee that the oracle price map is well-defined and (β-1)-smooth).","pith_extraction_headline":"In semiparametric contextual pricing, a scalar-index pilot reduces the problem to learning a one-dimensional smooth oracle price map whose nonparametric cost is minimax sharp."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15411/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"cited_work_retraction","ran_at":"2026-05-19T16:23:38.500435Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"citation_quote_validity","ran_at":"2026-05-19T15:50:47.046163Z","status":"completed","version":"0.1.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T15:31:17.809540Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T15:21:50.729399Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T14:21:54.151793Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T13:33:22.710623Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"a98d6834a08e72498c7e2ea78017d30c1bfc1a8ebad9b31fdb008a3decf4287b"},"references":{"count":56,"sample":[{"doi":"","year":1995,"title":"Proceedings of IEEE 36th Annual Foundations of Computer Science , pages=","work_id":"3c2cc0d0-f984-4881-8e32-dc965235e5bf","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"SIAM Journal on Computing , volume=","work_id":"b21af1d3-4acd-41ab-86a6-3c4f1b8bf812","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Revenue Maximization Under Sequential Price Competition Via The Estimation Of s-Concave Demand Functions","work_id":"f8539a7c-eacb-4fda-9db1-47d4519caa1f","ref_index":3,"cited_arxiv_id":"2503.16737","is_internal_anchor":true},{"doi":"","year":null,"title":"A Distribution-Free Theory of Nonparametric Regression , publisher =","work_id":"4a13409c-4581-45f7-a3fc-89e512ddd1a6","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"arXiv preprint arXiv:2405.06866 , year=","work_id":"0ceff58f-f03e-4bb4-aa5e-77276bcdfd0c","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":56,"snapshot_sha256":"650e6010060e5d0f6f6abe00149853ddb9f1b07a760eed381b9183440423089c","internal_anchors":1},"formal_canon":{"evidence_count":2,"snapshot_sha256":"9c3ac660644b1797fce0bfa3338c91c79d123057a33521f0c80caba98914b73c"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}