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Controlled Markov Chains with Utility Functions

In: Markov Processes and Controlled Markov Chains

Author

Listed:
  • Seiichi Iwamoto

    (Graduate School of Economics Kyushu University 27, Department of Economic Engineering)

  • Takayuki Ueno

    (Graduate School of Economics Kyushu University 27, Department of Economic Engineering)

  • Toshiharu Fujita

    (Kyushu Institute of Technology, Department of Electric, Electronic and Computer Engineering)

Abstract

In this paper we consider finite-stage stochastic optimization problems of utility criterion, which is the stochastic evaluation of associative reward through a utility function. We optimize the expected value of a utility criterion not in the class of Markov policies but in the class of general policies. We show that, by expanding the state space, an invariant imbedding approach yields an recursive relation between two adjacent optimal value functions. We show that the utility problem with a general policy is equivalent to a terminal problem with a Markov policy on the augmented state space. Finally it is shown that the utility problem has an optimal policy in the class of general policies on the original state space.

Suggested Citation

  • Seiichi Iwamoto & Takayuki Ueno & Toshiharu Fujita, 2002. "Controlled Markov Chains with Utility Functions," Springer Books, in: Zhenting Hou & Jerzy A. Filar & Anyue Chen (ed.), Markov Processes and Controlled Markov Chains, chapter 0, pages 135-149, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-0265-0_8
    DOI: 10.1007/978-1-4613-0265-0_8
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