## Finite State Markovian Decision Processes |

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Page 14

(R*, i, ha-1) - The first inequality follows from Lemma 1 and the last equation

follows from the induction assumption. The right-hand side is again independent

of ha-1. Hence, V.(R*, i, ha-1) = V.“(i), ie I. This proves the theorem.

1.

(R*, i, ha-1) - The first inequality follows from Lemma 1 and the last equation

follows from the induction assumption. The right-hand side is again independent

of ha-1. Hence, V.(R*, i, ha-1) = V.“(i), ie I. This proves the theorem.

**COROLLARY**1.

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0, ie I, and from Theorem 3 of Appendix C, xia > 0 for exactly one a e K, for each

i e I. This then implies D# = 1 or 0, i e I.

solution to the primal problem, (3.2) must hold. Proof: It follows from the

complementary ...

0, ie I, and from Theorem 3 of Appendix C, xia > 0 for exactly one a e K, for each

i e I. This then implies D# = 1 or 0, i e I.

**COROLLARY**3. For every optimalsolution to the primal problem, (3.2) must hold. Proof: It follows from the

complementary ...

Page 93

exists an Re CM such that HR(i) = HR(i). Proof. Since Xr"(i) = X,*(i) for every Tif R

is the policy constructed in Theorem 1, the

**CoROLLARY**1. Let HA(i) be the set of limit points of {X,*(i), T = 0, 1,...}; then thereexists an Re CM such that HR(i) = HR(i). Proof. Since Xr"(i) = X,*(i) for every Tif R

is the policy constructed in Theorem 1, the

**corollary**is evident. The significance ...### What people are saying - Write a review

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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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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