## 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 |

Copyright | |

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aeKi AOQL Appendix arbitrary assume backward induction Bellman Bibliographical Remarks compact constraints continuous function convex set Corollary defined denote Derman discounted cost criterion dual linear programming dual problem dynamic programming equality in 13 equations expected average cost expected cost expected discounted cost extreme point feasible solution finite number follows given HD(i Hence Hs(i i,jel inspection irreducible laws of motion Lemma lim inf Linear Programming Formulations linear programming problem Markov chain Markovian decision process maximize method of successive nondecreasing optimal first-passage problem optimal policy optimal solution optimal stopping policy improvement iteration policy improvement procedure policy in CD primal linear programming primal problem Proof random variables ReCD satisfies sequence of policy solving State-Action Frequencies stochastic process strict inequality holding successive approximations Suppose takes action theorem is proved transient traveling salesman problem Veinott vn(i vR(i vRl(i