{"paper":{"title":"Closing the Gap on the Sample Complexity of 1-Identification","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Matching lower and upper bounds close the sample complexity gap for 1-identification in bandits","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Wang Chi Cheung, Zitian Li","submitted_at":"2026-01-22T03:50:31Z","abstract_excerpt":"The 1-identification problem is a fundamental pure-exploration problem in multi-armed bandits. An agent aims to determine whether there exists an arm whose mean reward exceeds a known threshold $\\mu_0$, or to output \\textsf{None} otherwise. The agent must guarantee correctness with probability at least $1-\\delta$, while minimizing the expected number of arm pulls $\\mathbb{E}[\\tau]$. We study the 1-identification problem and make two main contributions. First, for instances with at least one qualified arm, we derive a new lower bound on $\\mathbb{E}[\\tau]$ via a novel optimization formulation. S"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"for instances with at least one qualified arm, we derive a new lower bound on E[τ] via a novel optimization formulation... upper bounds that match the lower bounds up to polynomial logarithmic factors uniformly over all instances.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The novel optimization formulation accurately captures the information-theoretic complexity of 1-identification, and standard concentration assumptions on rewards (e.g., sub-Gaussian) suffice for the upper-bound analysis to hold uniformly.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"New lower bound via optimization and matching upper bounds close the sample complexity gap for 1-identification in bandits with at least one qualified arm.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Matching lower and upper bounds close the sample complexity gap for 1-identification in bandits","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"239532076a5408742b5cc81ad7791e8eb1cd7e62c62427c500dff61b2ab302a1"},"source":{"id":"2601.15620","kind":"arxiv","version":2},"verdict":{"id":"3e300fe5-fddc-4e78-8692-c60c2b1f7a8b","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T12:25:13.321790Z","strongest_claim":"for instances with at least one qualified arm, we derive a new lower bound on E[τ] via a novel optimization formulation... upper bounds that match the lower bounds up to polynomial logarithmic factors uniformly over all instances.","one_line_summary":"New lower bound via optimization and matching upper bounds close the sample complexity gap for 1-identification in bandits with at least one qualified arm.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The novel optimization formulation accurately captures the information-theoretic complexity of 1-identification, and standard concentration assumptions on rewards (e.g., sub-Gaussian) suffice for the upper-bound analysis to hold uniformly.","pith_extraction_headline":"Matching lower and upper bounds close the sample complexity gap for 1-identification in bandits"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"488bb50a0526f3dcf8b306224460f50563bfdbe9271e926152505ffafc6af949"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}