{"paper":{"title":"Tight Bounds for $\\gamma$-Regret via the Decision-Estimation Coefficient","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Alexander Rakhlin, Margalit Glasgow","submitted_at":"2023-03-06T17:54:33Z","abstract_excerpt":"In this work, we give a statistical characterization of the $\\gamma$-regret for arbitrary structured bandit problems, the regret which arises when comparing against a benchmark that is $\\gamma$ times the optimal solution. The $\\gamma$-regret emerges in structured bandit problems over a function class $\\mathcal{F}$ where finding an exact optimum of $f \\in \\mathcal{F}$ is intractable. Our characterization is given in terms of the $\\gamma$-DEC, a statistical complexity parameter for the class $\\mathcal{F}$, which is a modification of the constrained Decision-Estimation Coefficient (DEC) of Foster"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.03327","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2303.03327/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}