2012
DOI: 10.4064/am39-2-6
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Deterministic optimal policies for Markov control processes with pathwise constraints

Abstract: This paper deals with discrete-time Markov control processes in Borel spaces with unbounded rewards. Under suitable hypotheses, we show that a randomized stationary policy is optimal for a certain expected constrained problem (ECP) if and only if it is optimal for the corresponding pathwise constrained problem (pathwise CP). Moreover, we show that a certain parametric family of unconstrained optimality equations yields convergence properties that lead to an approximation scheme which allows us to obtain constr… Show more

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Cited by 3 publications
(4 citation statements)
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“…Then V() ¼ min à 0 (Ã). (ii) (see [10,Theorem 4.8(b), (c) and Remark 2.2(ii) above. For each à 0, let f à 2 F be a stationary deterministic policy such that for every x 2 X, the action f à (x) 2 A(x) attains the maximum in the right-hand side of (16).…”
Section: Remark 33 By Assumptions 32(a) and 31(b3) We Have Thatmentioning
confidence: 88%
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“…Then V() ¼ min à 0 (Ã). (ii) (see [10,Theorem 4.8(b), (c) and Remark 2.2(ii) above. For each à 0, let f à 2 F be a stationary deterministic policy such that for every x 2 X, the action f à (x) 2 A(x) attains the maximum in the right-hand side of (16).…”
Section: Remark 33 By Assumptions 32(a) and 31(b3) We Have Thatmentioning
confidence: 88%
“…The following example is the sequel of the one given in [10,Section 6]). Suppose that the reward-per-stage function (51) and the cost-per-stage function (52) satisfy r 1 ¼ 1, r 2 ¼ 2, e ¼ 10 and c 1 ¼ c 2 ¼ 1, respectively.…”
Section: A Numerical Examplementioning
confidence: 99%
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