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A More General Pandora's Rule

Wednesday 13 November 2013, 4.30pm-5.30pm
NAB 2.06, New Academic Building

Professor Richard Weber

Churchill Professor of Mathematics for Operational Research, Statistical Laboratory, University of Cambridge

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Abstract:

In a famous model due to Weitzman (1979) an agent (Pandora) is presented with boxes containing prizes. She may open them however as she likes, discover prizes within, and optimally stop. Her aim is to maximize the expected value of the greatest prize she finds, minus the costs of opening boxes. This problem has an attractive solution by means of the so-called Pandora rule, and might be applied to searching for a research topic, house or job.

It does not, however, address the problem of a student who is searching for the subject to choose as her major and who benefits from all the courses she takes, not just from those taken once her major is chosen.  So motivated, we set out to discover whether there exist any problems for which a Pandora rule is optimal when the aim is to maximize is a more general function of all the revealed prizes.  We elucidate the connection between the Pandora rule and the Gittins index solution of an equivalent multi-armed bandit problem.

Although the Gittins index analysis tells most of the story, there do exist problems which are not equivalent to multi-armed bandits and for which a Pandora rule is optimal. We give a sufficient conditions that can be used to identify this and an example of its application.

Professor Weber's presentation can be found at:

http://www.statslab.cam.ac.uk/~rrw1/talks/LSEseminar13113.pdf

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