<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-01648665</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-26T08:28:33+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Sampling from a log-concave distribution with compact support with proximal Langevin Monte Carlo</title>
            <author role="aut">
              <persName>
                <forename type="first">Nicolas</forename>
                <surname>Brosse</surname>
              </persName>
              <email type="md5">c859706be2ea242ad6a2c953aa96cba4</email>
              <email type="domain">polytechnique.edu</email>
              <idno type="idhal" notation="numeric">1023761</idno>
              <idno type="halauthorid" notation="string">17005-1023761</idno>
              <affiliation ref="#struct-454595"/>
              <affiliation ref="#struct-89626"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Alain</forename>
                <surname>Durmus</surname>
              </persName>
              <email type="md5">01787fe59d16e0fb55fc0b40a5c095d7</email>
              <email type="domain">gmail.com</email>
              <idno type="idhal" notation="string">alain-oliviero-durmus</idno>
              <idno type="idhal" notation="numeric">1084098</idno>
              <idno type="halauthorid" notation="string">735110-1084098</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-2086-8611</idno>
              <idno type="IDREF">https://www.idref.fr/200536133</idno>
              <affiliation ref="#struct-162010"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Éric</forename>
                <surname>Moulines</surname>
              </persName>
              <email type="md5">6b1231a4aba97c57fa99606c0f031009</email>
              <email type="domain">tsi.enst.fr</email>
              <idno type="idhal" notation="numeric">1350242</idno>
              <idno type="halauthorid" notation="string">1222502-1350242</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-2058-0693</idno>
              <idno type="IDREF">https://www.idref.fr/076452476</idno>
              <idno type="VIAF">https://viaf.org/viaf/190144783095024669712</idno>
              <idno type="ISNI">http://isni.org/isni/000000045491609X</idno>
              <affiliation ref="#struct-454595"/>
              <affiliation ref="#struct-89626"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Marcelo</forename>
                <surname>Pereyra</surname>
              </persName>
              <email type="md5">8cb592d3b35ea4c059e0b9ecb4560fde</email>
              <email type="domain">ieee.org</email>
              <idno type="idhal" notation="numeric">1352362</idno>
              <idno type="halauthorid" notation="string">606759-1352362</idno>
              <idno type="ORCID">https://orcid.org/0000-0001-6438-6772</idno>
              <idno type="IDREF">https://www.idref.fr/17846760X</idno>
              <affiliation ref="#struct-198609"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Nicolas</forename>
                <surname>Brosse</surname>
              </persName>
              <email type="md5">850afa633246bc3d8323fb686b4212b0</email>
              <email type="domain">gmail.com</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2017-11-27 23:27:53</date>
              <date type="whenModified">2026-05-09 03:15:56</date>
              <date type="whenReleased">2017-11-28 11:56:49</date>
              <date type="whenProduced">2017</date>
              <date type="whenEndEmbargoed">2017-11-27</date>
              <ref type="file" target="https://inria.hal.science/hal-01648665v1/document">
                <date notBefore="2017-11-27"/>
              </ref>
              <ref type="file" n="1" target="https://inria.hal.science/hal-01648665v1/file/main.pdf" id="file-1648665-1691837">
                <date notBefore="2017-11-27"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="529893">
                <persName>
                  <forename>Nicolas</forename>
                  <surname>Brosse</surname>
                </persName>
                <email type="md5">850afa633246bc3d8323fb686b4212b0</email>
                <email type="domain">gmail.com</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-01648665</idno>
            <idno type="halUri">https://inria.hal.science/hal-01648665</idno>
            <idno type="halBibtex">brosse:hal-01648665</idno>
            <idno type="halRefHtml">&lt;i&gt;Proceedings of Machine Learning Research&lt;/i&gt;, 2017, 65, pp.319-342</idno>
            <idno type="halRef">Proceedings of Machine Learning Research, 2017, 65, pp.319-342</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-1648665-1691837"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="X">École polytechnique</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="ENST">Ecole Nationale Supérieure des Télécommunications</idno>
            <idno type="stamp" n="INRIA-SACLAY" corresp="INRIA">INRIA Saclay - Ile de France</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="TELECOM-PARISTECH" corresp="PARISTECH">Télécom Paris</idno>
            <idno type="stamp" n="X-CMAP" corresp="X">Centre de Mathématiques Appliquées (CMAP)</idno>
            <idno type="stamp" n="X-DEP-MATHA">Département de mathématiques appliquées de l’École polytechnique</idno>
            <idno type="stamp" n="PARISTECH">ParisTech</idno>
            <idno type="stamp" n="INRIA_TEST">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="TESTALAIN1">TESTALAIN1</idno>
            <idno type="stamp" n="CMAP">Centre de Mathématiques Appliquées (CMAP)</idno>
            <idno type="stamp" n="INRIA2">INRIA 2</idno>
            <idno type="stamp" n="INRIA-SACLAY-2015" corresp="UNIV-PARIS-SACLAY">INRIA-SACLAY-2015</idno>
            <idno type="stamp" n="TELECOM-PARISTECH-SACLAY" corresp="PARISTECH">TELECOM-PARISTECH-SACLAY</idno>
            <idno type="stamp" n="X-SACLAY" corresp="UNIV-PARIS-SACLAY">X-SACLAY</idno>
            <idno type="stamp" n="INRIA2017">INRIA2017</idno>
            <idno type="stamp" n="LTCI" corresp="TELECOM-PARISTECH">Laboratoire Traitement et Communication de l'Information</idno>
            <idno type="stamp" n="INSTITUTS-TELECOM">composantes instituts telecom </idno>
            <idno type="stamp" n="GS-COMPUTER-SCIENCE">Graduate School Computer Science</idno>
            <idno type="stamp" n="INRIA-ROYAUMEUNI">INRIA-ROYAUMEUNI</idno>
            <idno type="stamp" n="ACADEMIE-SCIENCES">Académie des sciences</idno>
            <idno type="stamp" n="INSTITUT-MINES-TELECOM">Institut Mines Telecom</idno>
            <idno type="stamp" n="IP-PARIS-DEPARTEMENT-MATHEMATIQUES">Département de Mathèmatiques</idno>
            <idno type="stamp" n="ACADEMIE-SCIENCES-PUBLICATIONS-MEMBRES" corresp="ACADEMIE-SCIENCES">Publications des membres, correspondants et associés étrangers de l'Académie des sciences</idno>
            <idno type="stamp" n="ACADEMIE-SCIENCES-PUBLICATIONS-MEMBRES-3" corresp="ACADEMIE-SCIENCES-PUBLICATIONS-MEMBRES">Publications des membres de l'Académie des sciences (lot 3)</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Sampling from a log-concave distribution with compact support with proximal Langevin Monte Carlo</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Nicolas</forename>
                    <surname>Brosse</surname>
                  </persName>
                  <email type="md5">c859706be2ea242ad6a2c953aa96cba4</email>
                  <email type="domain">polytechnique.edu</email>
                  <idno type="idhal" notation="numeric">1023761</idno>
                  <idno type="halauthorid" notation="string">17005-1023761</idno>
                  <affiliation ref="#struct-454595"/>
                  <affiliation ref="#struct-89626"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Alain</forename>
                    <surname>Durmus</surname>
                  </persName>
                  <email type="md5">01787fe59d16e0fb55fc0b40a5c095d7</email>
                  <email type="domain">gmail.com</email>
                  <idno type="idhal" notation="string">alain-oliviero-durmus</idno>
                  <idno type="idhal" notation="numeric">1084098</idno>
                  <idno type="halauthorid" notation="string">735110-1084098</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-2086-8611</idno>
                  <idno type="IDREF">https://www.idref.fr/200536133</idno>
                  <affiliation ref="#struct-162010"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Éric</forename>
                    <surname>Moulines</surname>
                  </persName>
                  <email type="md5">6b1231a4aba97c57fa99606c0f031009</email>
                  <email type="domain">tsi.enst.fr</email>
                  <idno type="idhal" notation="numeric">1350242</idno>
                  <idno type="halauthorid" notation="string">1222502-1350242</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-2058-0693</idno>
                  <idno type="IDREF">https://www.idref.fr/076452476</idno>
                  <idno type="VIAF">https://viaf.org/viaf/190144783095024669712</idno>
                  <idno type="ISNI">http://isni.org/isni/000000045491609X</idno>
                  <affiliation ref="#struct-454595"/>
                  <affiliation ref="#struct-89626"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Marcelo</forename>
                    <surname>Pereyra</surname>
                  </persName>
                  <email type="md5">8cb592d3b35ea4c059e0b9ecb4560fde</email>
                  <email type="domain">ieee.org</email>
                  <idno type="idhal" notation="numeric">1352362</idno>
                  <idno type="halauthorid" notation="string">606759-1352362</idno>
                  <idno type="ORCID">https://orcid.org/0000-0001-6438-6772</idno>
                  <idno type="IDREF">https://www.idref.fr/17846760X</idno>
                  <affiliation ref="#struct-198609"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">117525</idno>
                <idno type="issn">1938-7228</idno>
                <idno type="eissn">2640-3498</idno>
                <title level="j">Proceedings of Machine Learning Research</title>
                <imprint>
                  <publisher>PMLR</publisher>
                  <biblScope unit="volume">65</biblScope>
                  <biblScope unit="pp">319-342</biblScope>
                  <date type="datePub">2017</date>
                </imprint>
              </monogr>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <classCode scheme="halDomain" n="stat.me">Statistics [stat]/Methodology [stat.ME]</classCode>
              <classCode scheme="halDomain" n="stat.ap">Statistics [stat]/Applications [stat.AP]</classCode>
              <classCode scheme="halDomain" n="stat.th">Statistics [stat]/Statistics Theory [stat.TH]</classCode>
              <classCode scheme="halDomain" n="stat.ml">Statistics [stat]/Machine Learning [stat.ML]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>This paper presents a detailed theoretical analysis of the Langevin Monte Carlo sampling algorithm recently introduced in [DMP16] when applied to log-concave probability distributions that are restricted to a convex body K. This method relies on a regularisation procedure involving the Moreau-Yosida envelope of the indicator function associated with K. Explicit convergence bounds in total variation norm and in Wasserstein distance of order 1 are established. In particular, we show that the complexity of this algorithm given a first order oracle is polynomial in the dimension of the state space. Finally, some numerical experiments are presented to compare our method with competing MCMC approaches from the literature.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="researchteam" xml:id="struct-454595" status="OLD">
          <idno type="RNSR">201622140A</idno>
          <orgName>Modélisation en pharmacologie de population</orgName>
          <orgName type="acronym">XPOP</orgName>
          <date type="start">2016-01-01</date>
          <date type="end">2023-12-31</date>
          <desc>
            <address>
              <addrLine>Université Paris-Sud, Bâtiment 425 91405 Orsay Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/equipes/xpop</ref>
          </desc>
          <listRelation>
            <relation active="#struct-89626" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
            <relation active="#struct-300340" type="indirect"/>
            <relation active="#struct-563936" type="indirect"/>
            <relation name="UMR7641" active="#struct-441569" type="indirect"/>
            <relation active="#struct-1225635" type="direct"/>
            <relation active="#struct-118511" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-89626" status="VALID">
          <idno type="IdRef">197373461</idno>
          <idno type="ISNI">000000010944436X</idno>
          <idno type="RNSR">199719340P</idno>
          <idno type="ROR">https://ror.org/012e1xn46</idno>
          <idno type="Wikidata">Q16008922</idno>
          <orgName>Centre de Mathématiques Appliquées de l'Ecole polytechnique</orgName>
          <orgName type="acronym">CMAP</orgName>
          <date type="start">2005-01-01</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91128 Palaiseau Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://cmap.ip-paris.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
            <relation active="#struct-300340" type="direct"/>
            <relation active="#struct-563936" type="indirect"/>
            <relation name="UMR7641" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-162010" status="OLD">
          <orgName>Laboratoire Traitement et Communication de l'Information</orgName>
          <orgName type="acronym">LTCI</orgName>
          <desc>
            <address>
              <addrLine>46 rue Barrault F-75634 Paris Cedex 13</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.ltci.telecom-paristech.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300362" type="direct"/>
            <relation active="#struct-302102" type="direct"/>
            <relation name="UMR5141" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-198609" status="VALID">
          <orgName>Department of Actuarial Mathematics and Statistics [Edinburgh]</orgName>
          <desc>
            <address>
              <addrLine>Heriot-Watt University, Edinburgh, Scotland, UK EH14 4AS</addrLine>
              <country key="GB"/>
            </address>
            <ref type="url">http://www.macs.hw.ac.uk/departments/actuarial-maths-statistics.htm</ref>
          </desc>
          <listRelation>
            <relation active="#struct-32402" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300009" status="VALID">
          <idno type="ROR">https://ror.org/02kvxyf05</idno>
          <orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
          <orgName type="acronym">Inria</orgName>
          <desc>
            <address>
              <addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/en/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300340" status="VALID">
          <idno type="IdRef">027309320</idno>
          <idno type="ISNI">0000000121581279</idno>
          <idno type="ROR">https://ror.org/05hy3tk52</idno>
          <idno type="Wikidata">Q273626</idno>
          <orgName>École polytechnique</orgName>
          <orgName type="acronym">X</orgName>
          <date type="start">1794-03-11</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91128 Palaiseau Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.polytechnique.edu/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-563936" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-563936" status="VALID">
          <idno type="IdRef">238327159</idno>
          <idno type="ISNI">0000000502717600</idno>
          <idno type="ROR">https://ror.org/042tfbd02</idno>
          <idno type="Wikidata">Q48759778</idno>
          <orgName>Institut Polytechnique de Paris</orgName>
          <orgName type="acronym">IP Paris</orgName>
          <date type="start">2019-06-02</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91120 Palaiseau Cedex, France</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.ip-paris.fr</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
        <org type="department" xml:id="struct-1225635" status="VALID">
          <idno type="ROR">https://ror.org/026839t73</idno>
          <orgName>Centre Inria de l'Institut Polytechnique de Paris</orgName>
          <date type="start">2022-11-01</date>
          <desc>
            <address>
              <addrLine>1 rue Honoré d'Estienne d'Orves –Bâtiment Alan Turing –Campus de l'École Polytechnique –91120 Palaiseau</addrLine>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-118511" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-118511" status="VALID">
          <idno type="RNSR">200818248E</idno>
          <idno type="ROR">https://ror.org/0315e5x55</idno>
          <orgName>Centre Inria de Saclay</orgName>
          <desc>
            <address>
              <addrLine>1 rue Honoré d'Estienne d'OrvesBâtiment Alan TuringCampus de l'École Polytechnique91120 Palaiseau</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/centre/saclay</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300362" status="VALID">
          <idno type="ROR">https://ror.org/01naq7912</idno>
          <orgName>Télécom ParisTech</orgName>
          <date type="start">2008-01-01</date>
          <date type="end">2019-06-11</date>
          <desc>
            <address>
              <addrLine>46 rue Barrault 75634 Paris Cedex 13</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.telecom-paris.fr</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-302102" status="VALID">
          <idno type="IdRef">192427156</idno>
          <idno type="ISNI">000000012202567X</idno>
          <idno type="ROR">https://ror.org/025vp2923</idno>
          <idno type="Wikidata">Q27962533</idno>
          <orgName>Institut Mines-Télécom [Paris]</orgName>
          <orgName type="acronym">IMT</orgName>
          <date type="start">2012-03-01</date>
          <desc>
            <address>
              <addrLine>19 Place Marguerite Perey, 91120 Palaiseau</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.imt.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-32402" status="VALID">
          <orgName>Heriot-Watt University [Edinburgh]</orgName>
          <orgName type="acronym">HWU</orgName>
          <desc>
            <address>
              <addrLine>Edinburgh, Scotland, UK EH14 4AS</addrLine>
              <country key="GB"/>
            </address>
            <ref type="url">http://www.hw.ac.uk/home/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>