## Finite State Markovian Decision Processes |

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### Contents

Finite Horizon Expected Cost Minimization | 11 |

Some Existence Theorems | 19 |

Expected Average Cost Problem | 25 |

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Appendix arbitrary assume backward induction Bellman Bibliographical Remarks br(i Chapter closed convex compact computational constraints continuous function converges convex set Corollary defined denote denumerable Derman discounted cost criterion dual linear programming dual problem dynamic programming equations example expected average cost expected cost expected discounted cost extreme point feasible solution finite number follows given Hence inspection j|Yo laws of motion Lemma lim inf linear programming problem Markov chain Markovian decision process Math matrix maximize method of successive minimizes PR(i nondecreasing obtained optimal first-passage problem optimal policy optimal solution optimal stopping policy improvement iteration policy improvement procedure PR{Y primal problem ps(i qu(a qu(R random variables recurrent replace satisfies solving Stochastic games stochastic process strict inequality holding successive approximations Suppose takes action theorem is proved transient transition probabilities traveling salesman problem Veinott vo(i vs(i