Markov and semi-Markov decision models and optimal stopping

  • Manfred Schäl


We consider a system with a finite number of states i ϵ S. Periodically we observe the current state of the system, and then choose an action a from a set A of possible actions. As a result of the current state i and the chosen action a, the system moves to a new state j with the probability pij (a). As a further consequence, an immediate reward r(i, a) is earned. If the control process is stopped in a state i, then we obtain a terminal reward u (i). Thus, the underlying model is given by a tupel M = (S,A,p,r,u).
  1. (i)

    S stands for the state space and is assumed to be finite.

  2. (ii)

    A is the action space.

  3. (iii)

    pij (a) are the transition probabilities, where Σjϵs pij (a) = 1 for all i ϵ S, a ϵ A.

  4. (iv)

    r (i,a) is the real valued one-step reward.

  5. (v)

    u (i) is the real valued terminal reward or the utility function.



Decision Model Markov Decision Process Optimality Equation Average Reward Total Reward 
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Copyright information

© Springer Science+Business Media New York 1986

Authors and Affiliations

  • Manfred Schäl
    • 1
  1. 1.Institut für Angewandte MathematikUniversität BonnGermany

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