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Markov decision processes with noise-corrupted and delayed state observations

Author

Listed:
  • J L Bander

    (University of Michigan)

  • C C White

    (University of Michigan)

Abstract

We consider the partially observed Markov decision process with observations delayed by k time periods. We show that at stage t, a sufficient statistic is the probability distribution of the underlying system state at stage t - k and all actions taken from stage t - k through stage t - 1. We show that improved observation quality and/or reduced data delay will not decrease the optimal expected total discounted reward, and we explore the optimality conditions for three important special cases. We present a measure of the marginal value of receiving state observations delayed by (k - 1) stages rather than delayed by k stages. We show that in the limit as k →∞ the problem is equivalent to the completely unobserved case. We present numerical examples which illustrate the value of receiving state information delayed by k stages.

Suggested Citation

  • J L Bander & C C White, 1999. "Markov decision processes with noise-corrupted and delayed state observations," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(6), pages 660-668, June.
    • Handle: RePEc:pal:jorsoc:v:50:y:1999:i:6:d:10.1057_palgrave.jors.2600745
    DOI: 10.1057/palgrave.jors.2600745
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    Cited by:

    1. Michael Z. Spivey & Warren B. Powell, 2004. "The Dynamic Assignment Problem," Transportation Science, INFORMS, vol. 38(4), pages 399-419, November.

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