An Optimal Approximate Dynamic Programming Algorithm for the Lagged Asset Acquisition Problem

We consider a multistage asset acquisition problem where assets are purchased now, at a price that varies randomly over time, to be used to satisfy a random demand at a particular point in time in the future. We provide a rare proof of convergence for an approximate dynamic programming algorithm usi...

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Vydané v:Mathematics of operations research Ročník 34; číslo 1; s. 210 - 237
Hlavní autori: Nascimento, Juliana M, Powell, Warren B
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Linthicum INFORMS 01.02.2009
Institute for Operations Research and the Management Sciences
Predmet:
Adaptive control
Algorithms
approximate dynamic programming
Approximation
Asset acquisitions
Dynamic programming
Evaluation
Induction assumption
Integers
Mathematical functions
Mathematical induction
Mathematical inequalities
Operations research
Optimal policy
Stochastic analysis
stochastic approximation
stochastic learning and adaptive control
Studies
United States
ISSN:0364-765X, 1526-5471
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Abstract We consider a multistage asset acquisition problem where assets are purchased now, at a price that varies randomly over time, to be used to satisfy a random demand at a particular point in time in the future. We provide a rare proof of convergence for an approximate dynamic programming algorithm using pure exploitation, where the states we visit depend on the decisions produced by solving the approximate problem. The resulting algorithm does not require knowing the probability distribution of prices or demands, nor does it require any assumptions about its functional form. The algorithm and its proof rely on the fact that the true value function is a family of piecewise linear concave functions.
AbstractList We consider a multistage asset acquisition problem where assets are purchased now, at a price that varies randomly over time, to be used to satisfy a random demand at a particular point in time in the future. We provide a rare proof of convergence for an approximate dynamic programming algorithm using pure exploitation, where the states we visit depend on the decisions produced by solving the approximate problem. The resulting algorithm does not require knowing the probability distribution of prices or demands, nor does it require any assumptions about its functional form. The algorithm and its proof rely on the fact that the true value function is a family of piecewise linear concave functions.
We consider a multistage asset acquisition problem where assets are purchased now, at a price that varies randomly over time, to be used to satisfy a random demand at a particular point in time in the future. We provide a rare proof of convergence for an approximate dynamic programming algorithm using pure exploitation, where the states we visit depend on the decisions produced by solving the approximate problem. The resulting algorithm does not require knowing the probability distribution of prices or demands, nor does it require any assumptions about its functional form. The algorithm and its proof rely on the fact that the true value function is a family of piecewise linear concave functions. [PUBLICATION ABSTRACT]
Audience Academic
Author Nascimento, Juliana M
Powell, Warren B
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SubjectTerms Adaptive control
Algorithms
approximate dynamic programming
Approximation
Asset acquisitions
Dynamic programming
Evaluation
Induction assumption
Integers
Mathematical functions
Mathematical induction
Mathematical inequalities
Operations research
Optimal policy
Stochastic analysis
stochastic approximation
stochastic learning and adaptive control
Studies
Title An Optimal Approximate Dynamic Programming Algorithm for the Lagged Asset Acquisition Problem
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