@prefix dcat: <http://www.w3.org/ns/dcat#> .
@prefix dct: <http://purl.org/dc/terms/> .
@prefix foaf: <http://xmlns.com/foaf/0.1/> .
@prefix vcard: <http://www.w3.org/2006/vcard/ns#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00698517v1> a dcat:Dataset ;
    dct:description """
              We consider the problem of online stratified sampling for Monte Carlo integration of a function given a finite budget of $n$ noisy evaluations to the function. More precisely we focus on the problem of choosing the number of strata $K$ as a function of the budget $n$. We provide asymptotic and finite-time results on how an oracle that has access to the function would choose the partition optimally. In addition we prove a \\textit{lower bound} on the learning rate for the problem of stratified Monte-Carlo. As a result, we are able to state, by improving the bound on its performance, that algorithm MC-UCB, defined in~\\citep{MC-UCB}, is minimax optimal both in terms of the number of samples n and the number of strata K, up to a $\\sqrt{\\log(nK)}$. This enables to deduce a minimax optimal bound on the difference between the performance of the estimate outputted by MC-UCB, and the performance of the estimate outputted by the best oracle static strategy, on the class of Hölder continuous functions, and upt to a $\\sqrt{\\log(n)}$.
            """ ;
    dct:identifier "hal-00698517" ;
    dct:issued "2026-05-18T10:14:19.961628"^^xsd:dateTime ;
    dct:language "en" ;
    dct:modified "2026-05-18T10:14:19.961634"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Minimax Number of Strata for Online Stratified Sampling given Noisy Samples" ;
    dcat:contactPoint [ a vcard:Organization ;
            vcard:fn "CCSD" ] ;
    dcat:distribution <https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00698517v1/resource/8b583798-d40d-423e-a6c0-273c2937c504> ;
    dcat:keyword "acm-g-mathematics-of-computing",
        "infoeu-reposemanticspreprint",
        "mathmath-stmathematics-mathstatistics-mathst",
        "monte-carlo-integration",
        "online-learning",
        "preprints-working-papers-",
        "regret-bounds",
        "statthstatistics-statstatistics-theory-statth",
        "stratified-sampling" ;
    dcat:landingPage <https://inria.hal.science/hal-00698517> .

<https://rec.harvest-normandie.data4citizen.com/dataset/oai-hal-hal-00698517v1/resource/8b583798-d40d-423e-a6c0-273c2937c504> a dcat:Distribution ;
    dct:format "HTML" ;
    dct:issued "2026-05-18T10:14:20.015795"^^xsd:dateTime ;
    dct:modified "2026-05-18T10:14:19.913345"^^xsd:dateTime ;
    dct:title "Minimax Number of Strata for Online Stratified Sampling given Noisy Samples" ;
    dcat:accessURL <https://inria.hal.science/hal-00698517> .

<https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> a foaf:Agent ;
    foaf:name "test_moissonnage_selune" .

<https://inria.hal.science/hal-00698517> a foaf:Document .