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LP-Based Local Approximation for Markov Decision Problems

Please always quote using this URN:urn:nbn:de:0296-matheon-3307
  • The standard computational methods for computing the optimal value functions of Markov Decision Problems (MDP) require the exploration of the entire state space. This is practically infeasible for applications with huge numbers of states as they arise, e.g., from modeling the decisions in online optimization problems by MDPs. Exploiting column generation techniques, we propose and apply an LP-based method to determine an epsilon-approximation of the optimal value function at a given state by inspecting only states in a small neighborhood. In the context of online optimization problems, we use these methods in order to evaluate the quality of concrete policies with respect to given initial states. Moreover, the tools can also be used to obtain evidence of the impact of single decisions. This way, they can be utilized in the design of policies.

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Metadaten
Author:Stefan Heinz, Volker Kaibel, Matthias Peinhardt, Jörg Rambau, Andreas Tuchscherer
URN:urn:nbn:de:0296-matheon-3307
Referee:Rolf H. Möhring
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2006/08/31
Release Date:2006/06/29
Tag:
Institute:Zuse Institute Berlin (ZIB)
MSC-Classification:90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C40 Markov and semi-Markov decision processes
Preprint Number:343
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