Estimates of stability of Markov control processes with unbounded costs

Evgueni I. Gordienko; Francisco Salem-Silva

Displaying similar documents to “Estimates of stability of Markov control processes with unbounded costs”

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...

Estimates for perturbations of average Markov decision processes with a minimal state and upper bounded by stochastically ordered Markov chains

Raúl Montes-de-Oca, Francisco Salem-Silva (2005)

Kybernetika

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This paper deals with Markov decision processes (MDPs) with real state space for which its minimum is attained, and that are upper bounded by (uncontrolled) stochastically ordered (SO) Markov chains. We consider MDPs with (possibly) unbounded costs, and to evaluate the quality of each policy, we use the objective function known as the average cost. For this objective function we consider two Markov control models $ℙ$ and $ℙ_{1}$ . $ℙ$ and $ℙ_{1}$ have the same components except for the transition laws....

A semimartingale characterization of average optimal stationary policies for Markov decision processes.

Zhu, Quanxin, Guo, Xianping (2006)

Journal of Applied Mathematics and Stochastic Analysis

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Ergodic control of partially observed Markov processes with equivalent transition probabilities

Łukasz Stettner (1993)

Applicationes Mathematicae

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Optimal control with long run average cost functional of a partially observed Markov process is considered. Under the assumption that the transition probabilities are equivalent, the existence of the solution to the Bellman equation is shown, with the use of which optimal strategies are constructed.

On self-optimizing control of Markov processes

Petr Mandl (1985)

Banach Center Publications

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Average cost Markov control processes with weighted norms: existence of canonical policies

Evgueni Gordienko, Onésimo Hernández-Lerma (1995)

Applicationes Mathematicae

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This paper considers discrete-time Markov control processes on Borel spaces, with possibly unbounded costs, and the long run average cost (AC) criterion. Under appropriate hypotheses on weighted norms for the cost function and the transition law, the existence of solutions to the average cost optimality inequality and the average cost optimality equation are shown, which in turn yield the existence of AC-optimal and AC-canonical policies respectively.