The Linear Programming Approach to Approximate Dynamic Programming

The curse of dimensionality gives rise to prohibitive computational requirements that render infeasible the exact solution of large-scale stochastic control problems. We study an efficient method based on linear programming for approximating solutions to such problems. The approach "fits"...

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Bibliographic Details
Published in:Operations research Vol. 51; no. 6; pp. 850 - 865
Main Authors: de Farias, D. P, Van Roy, B
Format: Journal Article
Language:English
Published: Linthicum INFORMS 01.11.2003
Institute for Operations Research and the Management Sciences
Subjects:
Algorithms
Approximation
Approximation theory
Average cost
Dynamic programming
Dynamic programming/optimal control: approximations/large-scale problems
Error bounds
Liapunov functions
Linear programming
Machine learning
Mathematical vectors
Methods
Operations research
Process controls
Queueing networks
Queues, algorithms: control of queueing networks
Queuing
Studies
ISSN:0030-364X, 1526-5463
Online Access:Get full text
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Summary:The curse of dimensionality gives rise to prohibitive computational requirements that render infeasible the exact solution of large-scale stochastic control problems. We study an efficient method based on linear programming for approximating solutions to such problems. The approach "fits" a linear combination of pre-selected basis functions to the dynamic programming cost-to-go function. We develop error bounds that offer performance guarantees and also guide the selection of both basis functions and "state-relevance weights" that influence quality of the approximation. Experimental results in the domain of queueing network control provide empirical support for the methodology.
Bibliography:SourceType-Scholarly Journals-1
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ISSN:0030-364X
1526-5463
DOI:10.1287/opre.51.6.850.24925