Displaying similar documents to “Approximation and estimation in Markov control processes under a discounted criterion”

Adaptive control for discrete-time Markov processes with unbounded costs: Discounted criterion

Evgueni I. Gordienko, J. Adolfo Minjárez-Sosa (1998)

Kybernetika

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We study the adaptive control problem for discrete-time Markov control processes with Borel state and action spaces and possibly unbounded one-stage costs. The processes are given by recurrent equations x t + 1 = F ( x t , a t , ξ t ) , t = 0 , 1 , ... with i.i.d. ℜ k -valued random vectors ξ t whose density ρ is unknown. Assuming observability of ξ t we propose the procedure of statistical estimation of ρ that allows us to prove discounted asymptotic optimality of two types of adaptive policies used early for the processes with bounded...

Approximation, estimation and control of stochastic systems under a randomized discounted cost criterion

Juan González-Hernández, Raquiel R. López-Martínez, J. Adolfo Minjárez-Sosa (2009)

Kybernetika

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The paper deals with a class of discrete-time stochastic control processes under a discounted optimality criterion with random discount rate, and possibly unbounded costs. The state process x t and the discount process α t evolve according to the coupled difference equations x t + 1 = F ( x t , α t , a t , ξ t ) , α t + 1 = G ( α t , η t ) where the state and discount disturbance processes { ξ t } and { η t } are sequences of i.i.d. random variables with densities ρ ξ and ρ η respectively. The main objective is to introduce approximation algorithms...

Deterministic optimal policies for Markov control processes with pathwise constraints

Armando F. Mendoza-Pérez, Onésimo Hernández-Lerma (2012)

Applicationes Mathematicae

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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...