{"paper":{"title":"Open Problem: Best Arm Identification: Almost Instance-Wise Optimality and the Gap Entropy Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Jian Li, Lijie Chen","submitted_at":"2016-05-27T00:23:39Z","abstract_excerpt":"The best arm identification problem (BEST-1-ARM) is the most basic pure exploration problem in stochastic multi-armed bandits. The problem has a long history and attracted significant attention for the last decade. However, we do not yet have a complete understanding of the optimal sample complexity of the problem: The state-of-the-art algorithms achieve a sample complexity of $O(\\sum_{i=2}^{n} \\Delta_{i}^{-2}(\\ln\\delta^{-1} + \\ln\\ln\\Delta_i^{-1}))$ ($\\Delta_{i}$ is the difference between the largest mean and the $i^{th}$ mean), while the best known lower bound is $\\Omega(\\sum_{i=2}^{n} \\Delta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08481","kind":"arxiv","version":1},"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"}