## 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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AOQL Appendix aR(i arbitrary assume backward induction Bellman Bibliographical Remarks Chapter compact compact spaces computational constraints continuous function converges convex set Corollary defined denote 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 HD(i Hence HR(i Hs(i inspection laws of motion Lemma lim inf linear programming problem Markov chain Markovian decision process matrix maximize method of successive nondecreasing nonnegative optimal first-passage problem optimal policy optimal solution optimal stopping policy improvement iteration policy improvement procedure policy in CD primal problem random variables ReC Proof satisfies solving stochastic process strict inequality holding successive approximations super-regular function Suppose takes action theorem is proved transient transition probabilities traveling salesman problem Veinott vn(i Vn(R XTR(i