{"paper":{"title":"Normal Bandits of Unknown Means and Variances: Asymptotic Optimality, Finite Horizon Regret Bounds, and a Solution to an Open Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Junya Honda, Michael N. Katehakis, Wesley Cowan","submitted_at":"2015-04-22T14:30:13Z","abstract_excerpt":"Consider the problem of sampling sequentially from a finite number of $N \\geq 2$ populations, specified by random variables $X^i_k$, $ i = 1,\\ldots , N,$ and $k = 1, 2, \\ldots$; where $X^i_k$ denotes the outcome from population $i$ the $k^{th}$ time it is sampled. It is assumed that for each fixed $i$,\n  $\\{ X^i_k \\}_{k \\geq 1}$ is a sequence of i.i.d. normal random variables, with unknown mean $\\mu_i$ and unknown variance $\\sigma_i^2$.\n  The objective is to have a policy $\\pi$ for deciding from which of the $N$ populations to sample form at any time $n=1,2,\\ldots$ so as to maximize the expect"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05823","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":""},"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"}