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A discrete on-line monotone estimation algorithm

Papadaki, Katerina P. and Powell, Warren B. (2003) A discrete on-line monotone estimation algorithm. Operational Research working papers, LSEOR 03.73. Department of Operational Research, London School of Economics and Political Science, London, UK. ISBN 0753016958

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Abstract

In the paper Papadaki & Powell (2002) we introduced an adaptive dynamic programming algorithm to estimate the monotone value functions for the problem of batch service of homogeneous customers at a service station. The algorithm uses an updating scheme that takes advantage of the monotone structure of the function by imposing a monotonicity-preserving step. In this paper we introduce an algorithm (DOME) that uses this monotonicity-preserving step to approximate discrete monotone functions. Our algorithm requires sampling a discrete function and using Monte Carlo estimates to update the function. It is a known result that sampling a discrete function on each point of its domain infinitely often converges to the correct function as long as standard requirements on the stepsize are maintained. Imposing a monotonicity-preserving step raises anew the question of convergence. We prove convergence of such an algorithm.

Item Type: Monograph (Working Paper)
Official URL: http://www.lse.ac.uk/collections/operationalResear...
Additional Information: © 2003 London School of Economics and Political Science
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Research centres and groups > Management Science Group
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Identification Number: LSEOR 03.73
Date Deposited: 16 Feb 2009 09:49
URL: http://eprints.lse.ac.uk/22744/

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