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Reinforcement learning from comparisons: Three alternatives are enough, two are not

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Listed:
  • Benoit Laslier

    (ICJ - Institut Camille Jordan - ECL - École Centrale de Lyon - Université de Lyon - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique, PSPM - Probabilités, statistique, physique mathématique - ICJ - Institut Camille Jordan - ECL - École Centrale de Lyon - Université de Lyon - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - INSA Lyon - Institut National des Sciences Appliquées de Lyon - Université de Lyon - INSA - Institut National des Sciences Appliquées - UJM - Université Jean Monnet - Saint-Étienne - CNRS - Centre National de la Recherche Scientifique)

  • Jean-François Laslier

    (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

Abstract

This paper deals with two generalizations of the Polya urn model where, instead of sampling one ball from the urn at each time, we sample two or three balls. The processes are defined on the basis of the problem of finding the best alternative using pairwise comparisons which are not necessarily transitive: they can be thought of as evolutionary processes that tend to reinforce currently efficient alternatives. The two processes exhibit different behaviors: with three balls sampled, we prove almost sure convergence towards the unique optimal solution of the comparisons problem while, in some cases, the process with two balls sampled has almost surely no limit. This is an example of a natural reinforcement model with no exchangeability whose asymptotic behavior can be precisely characterized.

Suggested Citation

  • Benoit Laslier & Jean-François Laslier, 2017. "Reinforcement learning from comparisons: Three alternatives are enough, two are not," Post-Print halshs-01630231, HAL.
    • Handle: RePEc:hal:journl:halshs-01630231
    DOI: 10.1214/16-AAP1271
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    Cited by:

    1. Florian Brandl & Felix Brandt, 2021. "A Natural Adaptive Process for Collective Decision-Making," Papers 2103.14351, arXiv.org, revised Mar 2024.
    2. Brandl, Florian & Brandt, Felix, 2024. "A natural adaptive process for collective decision-making," Theoretical Economics, Econometric Society, vol. 19(2), May.
    3. Crimaldi, Irene & Louis, Pierre-Yves & Minelli, Ida G., 2022. "An urn model with random multiple drawing and random addition," Stochastic Processes and their Applications, Elsevier, vol. 147(C), pages 270-299.

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