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Markov Decision Processes

In: Hamiltonian Cycle Problem and Markov Chains

Author

Listed:
  • Vivek S. Borkar

    (IIT, Powai)

  • Vladimir Ejov

    (Flinders University)

  • Jerzy A. Filar

    (Flinders University)

  • Giang T. Nguyen

    (Université libre de Bruxelles)

Abstract

Markov chains are useful in describing many discrete event stochastic processes; however, they are not exible enough to model situations where we have to make decisions to control the future trajectories of the system. For this reason, the theory of Markov decision processes (MDPs), also known as controlled Markov chains, has been developed. In particular, in the context of this book, we observe that in any given graph Hamiltonian cycles (if any) correspond to a family of spanning subgraphs inducing very special Markov chains whose probability transition matrices are a subset of permutation matrices possessing only a single ergodic class.

Suggested Citation

  • Vivek S. Borkar & Vladimir Ejov & Jerzy A. Filar & Giang T. Nguyen, 2012. "Markov Decision Processes," International Series in Operations Research & Management Science, in: Hamiltonian Cycle Problem and Markov Chains, edition 127, chapter 0, pages 49-66, Springer.
    • Handle: RePEc:spr:isochp:978-1-4614-3232-6_4
    DOI: 10.1007/978-1-4614-3232-6_4
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