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  <doc>
    <id>8398</id>
    <completedYear/>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1</pageFirst>
    <pageLast>23</pageLast>
    <pageNumber/>
    <edition/>
    <issue>284</issue>
    <volume>22</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Linear Bandits on Uniformly Convex Sets</title>
    <abstract language="eng">Linear bandit algorithms yield O~(n√T) pseudo-regret bounds on compact convex action sets K⊂Rn and two types of structural assumptions lead to better pseudo-regret bounds. When K is the simplex or an ℓp ball with p∈]1,2], there exist bandits algorithms with O~(√n√T) pseudo-regret bounds. Here, we derive bandit algorithms for some strongly convex sets beyond ℓp balls that enjoy pseudo-regret bounds of O~(√n√T), which answers an open question from [BCB12, §5.5.]. Interestingly, when the action set is uniformly convex but not necessarily strongly convex, we obtain pseudo-regret bounds with a dimension dependency smaller than O(√n). However, this comes at the expense of asymptotic rates in T varying between O(√T) and O(T).</abstract>
    <parentTitle language="eng">Journal of Machine Learning Research</parentTitle>
    <identifier type="url">https://www.jmlr.org/papers/v22/21-0277.html</identifier>
    <enrichment key="PeerReviewed">no</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Thomas Kerdreux</author>
    <submitter> Kerdreux</submitter>
    <author>Christophe Roux</author>
    <author>Alexandre d'Aspremont</author>
    <author>Sebastian Pokutta</author>
    <collection role="persons" number="pokutta">Pokutta, Sebastian</collection>
    <collection role="institutes" number="ais2t">AI in Society, Science, and Technology</collection>
    <collection role="persons" number="Roux">Roux, Christophe</collection>
    <collection role="projects" number="Math+AA3-7">Math+AA3-7</collection>
  </doc>
</export-example>
