Robbins' problem (original) (raw)
Le problème de Robbins, aussi appelé quatrième problème de la secrétaire, est un problème mathématique de théorie des probabilités et plus particulièrement de (en). Il doit son nom au mathématicien Herbert Robbins qui l'a énoncé la première fois en 1990. Le problème de Robbins reste jusqu'à ce jour encore ouvert.
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| dbo:abstract | Le problème de Robbins, aussi appelé quatrième problème de la secrétaire, est un problème mathématique de théorie des probabilités et plus particulièrement de (en). Il doit son nom au mathématicien Herbert Robbins qui l'a énoncé la première fois en 1990. Le problème de Robbins reste jusqu'à ce jour encore ouvert. (fr) In probability theory, Robbins' problem of optimal stopping, named after Herbert Robbins, is sometimes referred to as the fourth secretary problem or the problem of minimizing the expected rank with full information. Its statement is as follows. Let X1, ... , Xn be independent, identically distributed random variables, uniform on [0, 1]. We observe the Xk's sequentially and must stop on exactly one of them. No recall of preceding observations is permitted. What stopping rule minimizes the expected rank of the selected observation, and what is its corresponding value? The general solution to this full-information expected rank problem is unknown. The major difficulty is that the problem is fully history-dependent, that is, the optimal rule depends at every stage on all preceding values, and not only on simpler sufficient statistics of these. Only bounds are known for the limiting value v as n goes to infinity, namely 1.908 < v < 2.329. It is known that there is some room to improve the lower bound by further computations for a truncated version of the problem. It is still not known how to improve on the upper bound which stems from the subclass of memoryless threshold rules. (en) |
| dbo:wikiPageExternalLink | http://cat.inist.fr/%3FaModele=afficheN&cpsidt=3259597 https://web.archive.org/web/20110607164808/http:/projecteuclid.org/DPubS%3Fservice=UI&version=1.0&verb=Display&handle=euclid.jap%2F1110381374 |
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| dbo:wikiPageWikiLink | dbr:Continuous_uniform_distribution dbr:Thomas_S._Ferguson dbr:Optimal_stopping dbr:Amherst,_Massachusetts dbr:Expected_value dbr:Israel_Journal_of_Mathematics dbr:Probability_theory dbr:Random_variable dbr:Herbert_Robbins dbc:Stochastic_optimization dbr:Secretary_problem dbr:Sequential_analysis dbr:F._Thomas_Bruss dbr:International_Conference_on_Search_and_Selection_in_Real_Time |
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| dct:subject | dbc:Stochastic_optimization |
| rdfs:comment | Le problème de Robbins, aussi appelé quatrième problème de la secrétaire, est un problème mathématique de théorie des probabilités et plus particulièrement de (en). Il doit son nom au mathématicien Herbert Robbins qui l'a énoncé la première fois en 1990. Le problème de Robbins reste jusqu'à ce jour encore ouvert. (fr) In probability theory, Robbins' problem of optimal stopping, named after Herbert Robbins, is sometimes referred to as the fourth secretary problem or the problem of minimizing the expected rank with full information. Its statement is as follows. Let X1, ... , Xn be independent, identically distributed random variables, uniform on [0, 1]. We observe the Xk's sequentially and must stop on exactly one of them. No recall of preceding observations is permitted. What stopping rule minimizes the expected rank of the selected observation, and what is its corresponding value? (en) |
| rdfs:label | Problème de Robbins (fr) Robbins' problem (en) |
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