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On the optimal stopping time of learning
Mälardalen University, School of Education, Culture and Communication.
2008 (English)Licentiate thesis, comprehensive summary (Other scientific)
Abstract [en]

 The goal of this thesis is to study the economics of computational learning. Attention is also paid to applications of computational learning models, especially Valiant's so-called `probably approximately correctly' (PAC) learning model, in econometric situations.

Specifically, an economically reasonable stopping time model of learning is the subject of two attached papers. In the rst paper, Paper A, the economics of PAC learning are considered. It is shown how a general form of the optimal stopping time bounds can be achieved using the PAC convergence rates for a `pessimistic-rational' learner in the most standard binary case of passive supervised PAC model of finite Vapnik-Chervonenkis (VC) dimension.

 

The second paper, Paper B, states precisely and improves the ideas introduced in Paper A and tests them in a specific and mathematically simple case. Using the maxmin procedure of Gilboa and Schmeidler the bounds for the stopping time are expressed in terms of the largest expected error of recall, and thus, effectively, in terms of the least expected reward. The problem of locating a real number θ by testing whether xi ≤ θ , with xi drawn from an calculated for a range of term rates, sample costs and rewards/penalties from a recall ae included. The standard econometric situations, such as product promotion, market research, credit risk assessment, and bargaining and tenders, where such bounds could be of interest, are pointed. 

These two papers are the essence of this thesis, and form it togheter with an introduction to the subject of learning.

Abstract [sv]

Målet med denna avhandling är att studera optimering av inlärning när det finns kostnader. Speciellt studerar jag Valiants så kallade PAC-inlärningsmodell  (Probably Approximately Correctly), ofta använd inom datavetenskap. I två artiklar behandlar jag hur länge, ur ekonomisk synvinkel, inlärningsperioden bör fortsätta.

I den första artikeln visar vi hur en generell form av begränsningar av den optimala inlärningsperioden kan fås med hjälp av PAC-konvergenshastigheten för en ’pessimistiskt rationell’ studerande (i det vanligaste binära fallet av passiv PAC-inlärningsmodell med ändlig VC-dimension).

I den andra artikeln fördjupar och förbättrar vi idéerna från den första artikeln, och testar dem i en specifik situation som är matematiskt enkel. Med hjälp av Gilboa – Schmeidlers max - minprocedur  uttrycker vi begränsningarna av den optimala inlärningsperioden som funktion av det största förväntade felet och därmed som funktion av den minsta förväntade belöningen. Vi diskuterar problemet med att hitta ett reellt tal θ genom testning av huruvida xi ≤ θ, där xi dras från en okänd fördelning. Här tar vi också upp exempel på begränsningar av inlärningsperioden, beräknade för en mängd av diskontovärden, stickprovskostnader och belöning/straff för erinran, samt en del vanliga ekonometriska situationer där sådana begränsningar är av intresse, såsom marknadsföring av produkter, marknadsanalys, kreditriskskattning och offertförhandling.

Avhandlingen består i huvuddel av dessa två artiklar samt en kort introduktion till ekonomiska, matematiska och datavetenskapliga inlärningsmodeller.

 

Place, publisher, year, edition, pages
Mälardalens högskola: Västerås , 2008. , p. 28
Series
Mälardalen University Press Licentiate Theses, ISSN 1651-9256 ; 96
Keywords
stopping time
National Category
Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-1531ISBN: 978-91-86135-12-6 (print)OAI: oai:DiVA.org:mdh-1530DiVA, id: diva2:114254
Presentation
Gamma, Högskoleplan 1, Västerås (Swedish)
Opponent
Supervisors
Available from: 2008-11-10 Created: 2008-10-29 Last updated: 2008-11-17Bibliographically approved
List of papers
1. Learning a real number, rationally
Open this publication in new window or tab >>Learning a real number, rationally
2007 (English)Report (Other academic)
Place, publisher, year, edition, pages
Department of Mathematics and Physics, Mälardalen University, 2007. p. 32
Series
Research reports MDH/IMA ; 3
Keywords
ambiguity, learning, multiple prior, stopping time, utility
National Category
Mathematics
Identifiers
urn:nbn:se:mdh:diva-2972 (URN)
Available from: 2008-03-08 Created: 2008-03-08 Last updated: 2015-07-30Bibliographically approved
2. When to stop learning?: Bounding the stopping time in the PAC model
Open this publication in new window or tab >>When to stop learning?: Bounding the stopping time in the PAC model
2001 (Swedish)In: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 7, no 23, p. 5-12Article in journal (Refereed) Published
National Category
Mathematics
Identifiers
urn:nbn:se:mdh:diva-2976 (URN)
Available from: 2008-03-08 Created: 2008-03-08 Last updated: 2015-07-08Bibliographically approved

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CiteExportLink to record
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Citation style
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