Optimal Adaptive Policies for Sequential Allocation Problems
Consider the problem of sequential sampling frommstatistical populations to maximize the expected sum of outcomes in the long run. Under suitable assumptions on the unknown parameters[formula], it is shown that there exists a classCRof adaptive policies with the following properties: (i) The expecte...
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| Veröffentlicht in: | Advances in applied mathematics 1996-06, Vol.17 (2), p.122-142 |
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| container_title | Advances in applied mathematics |
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| creator | Burnetas, Apostolos N. Katehakis, Michael N. |
| description | Consider the problem of sequential sampling frommstatistical populations to maximize the expected sum of outcomes in the long run. Under suitable assumptions on the unknown parameters[formula], it is shown that there exists a classCRof adaptive policies with the following properties: (i) The expectednhorizon reward[formula]under any policy π0inCRis equal to[formula], asn→∞, where[formula]is the largest population mean and[formula]is a constant. (ii) Policies inCRare asymptotically optimal within a larger classCUFof “uniformly fast convergent” policies in the sense that[formula], for any π∈CUFand any[formula]such that[formula]. Policies inCRare specified via easily computable indices, defined as unique solutions to dual problems that arise naturally from the functional form of[formula]. In addition, the assumptions are verified for populations specified by nonparametric discrete univariate distributions with finite support. In the case of normal populations with unknown means and variances, we leave as an open problem the verification of one assumption. |
| doi_str_mv | 10.1006/aama.1996.0007 |
| format | Article |
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Under suitable assumptions on the unknown parameters[formula], it is shown that there exists a classCRof adaptive policies with the following properties: (i) The expectednhorizon reward[formula]under any policy π0inCRis equal to[formula], asn→∞, where[formula]is the largest population mean and[formula]is a constant. (ii) Policies inCRare asymptotically optimal within a larger classCUFof “uniformly fast convergent” policies in the sense that[formula], for any π∈CUFand any[formula]such that[formula]. Policies inCRare specified via easily computable indices, defined as unique solutions to dual problems that arise naturally from the functional form of[formula]. In addition, the assumptions are verified for populations specified by nonparametric discrete univariate distributions with finite support. 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Under suitable assumptions on the unknown parameters[formula], it is shown that there exists a classCRof adaptive policies with the following properties: (i) The expectednhorizon reward[formula]under any policy π0inCRis equal to[formula], asn→∞, where[formula]is the largest population mean and[formula]is a constant. (ii) Policies inCRare asymptotically optimal within a larger classCUFof “uniformly fast convergent” policies in the sense that[formula], for any π∈CUFand any[formula]such that[formula]. Policies inCRare specified via easily computable indices, defined as unique solutions to dual problems that arise naturally from the functional form of[formula]. In addition, the assumptions are verified for populations specified by nonparametric discrete univariate distributions with finite support. In the case of normal populations with unknown means and variances, we leave as an open problem the verification of one assumption.</description><subject>Exact sciences and technology</subject><subject>Mathematics</subject><subject>Probability and statistics</subject><subject>Sciences and techniques of general use</subject><subject>Sequential methods</subject><subject>Statistics</subject><issn>0196-8858</issn><issn>1090-2074</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1996</creationdate><recordtype>article</recordtype><recordid>eNp1kM1LwzAYh4MoOKdXzz2It9ZkadIEvIzhFww2UM8hTd5CJG1m0g38703Z8ObpfQ_P7_14ELoluCIY8wete10RKXmFMW7O0IxgicsFbupzNMNE8lIIJi7RVUpfmZALTmfocbMbXa99sbQ6dwcotsE74yAVXYjFO3zvYRjdBHgfjB5dGIptDK2HPl2ji077BDenOkefz08fq9dyvXl5Wy3XpaGCj2XdEWlaLQzhpG1sY2oLUtTYEjCmZRYol8JyZkiDOdRdwyVrtQXobF0Lq-kc3R_n7mLI96RR9S4Z8F4PEPZJUcoEY5JnsDqCJoaUInRqF_N38UcRrCZJapKkJklqkpQDd6fJOhntu6gH49JfipKF5IxkTBwxyF8eHESVsqLBgHURzKhscP9t-AWDSXtF</recordid><startdate>19960601</startdate><enddate>19960601</enddate><creator>Burnetas, Apostolos N.</creator><creator>Katehakis, Michael N.</creator><general>Elsevier Inc</general><general>Elsevier</general><scope>6I.</scope><scope>AAFTH</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>19960601</creationdate><title>Optimal Adaptive Policies for Sequential Allocation Problems</title><author>Burnetas, Apostolos N. ; Katehakis, Michael N.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c386t-4f19cba8c161b7d7c4de9840d1eccb5de3698d65c1706e4f7695badeefd448da3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1996</creationdate><topic>Exact sciences and technology</topic><topic>Mathematics</topic><topic>Probability and statistics</topic><topic>Sciences and techniques of general use</topic><topic>Sequential methods</topic><topic>Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Burnetas, Apostolos N.</creatorcontrib><creatorcontrib>Katehakis, Michael N.</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Advances in applied mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Burnetas, Apostolos N.</au><au>Katehakis, Michael N.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Optimal Adaptive Policies for Sequential Allocation Problems</atitle><jtitle>Advances in applied mathematics</jtitle><date>1996-06-01</date><risdate>1996</risdate><volume>17</volume><issue>2</issue><spage>122</spage><epage>142</epage><pages>122-142</pages><issn>0196-8858</issn><eissn>1090-2074</eissn><coden>AAPMEF</coden><abstract>Consider the problem of sequential sampling frommstatistical populations to maximize the expected sum of outcomes in the long run. Under suitable assumptions on the unknown parameters[formula], it is shown that there exists a classCRof adaptive policies with the following properties: (i) The expectednhorizon reward[formula]under any policy π0inCRis equal to[formula], asn→∞, where[formula]is the largest population mean and[formula]is a constant. (ii) Policies inCRare asymptotically optimal within a larger classCUFof “uniformly fast convergent” policies in the sense that[formula], for any π∈CUFand any[formula]such that[formula]. Policies inCRare specified via easily computable indices, defined as unique solutions to dual problems that arise naturally from the functional form of[formula]. In addition, the assumptions are verified for populations specified by nonparametric discrete univariate distributions with finite support. 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| ispartof | Advances in applied mathematics, 1996-06, Vol.17 (2), p.122-142 |
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| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; ScienceDirect Journals (5 years ago - present) |
| subjects | Exact sciences and technology Mathematics Probability and statistics Sciences and techniques of general use Sequential methods Statistics |
| title | Optimal Adaptive Policies for Sequential Allocation Problems |
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