Displaying similar documents to “Infinite-horizon Markov control processes with undiscounted cost criteria: from average to overtaking optimality”

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...

On adaptive control of a partially observed Markov chain

Giovanni Di Masi, Łukasz Stettner (1994)

Applicationes Mathematicae

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A control problem for a partially observable Markov chain depending on a parameter with long run average cost is studied. Using uniform ergodicity arguments it is shown that, for values of the parameter varying in a compact set, it is possible to consider only a finite number of nearly optimal controls based on the values of actually computable approximate filters. This leads to an algorithm that guarantees nearly selfoptimizing properties without identifiability conditions. The algorithm...

Average cost Markov control processes with weighted norms: value iteration

Evgueni Gordienko, Onésimo Hernández-Lerma (1995)

Applicationes Mathematicae

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This paper shows the convergence of the value iteration (or successive approximations) algorithm for average cost (AC) Markov control processes on Borel spaces, with possibly unbounded cost, under appropriate hypotheses on weighted norms for the cost function and the transition law. It is also shown that the aforementioned convergence implies strong forms of AC-optimality and the existence of forecast horizons.

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.

Nonparametric adaptive control for discrete-time Markov processes with unbounded costs under average criterion

J. Minjárez-Sosa (1999)

Applicationes Mathematicae

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We introduce average cost optimal adaptive policies in a class of discrete-time Markov control processes with Borel state and action spaces, allowing unbounded costs. The processes evolve according to the system equations x t + 1 = F ( x t , a t , ξ t ) , t=1,2,..., with i.i.d. ℝ k -valued random vectors ξ t , which are observable but whose density ϱ is unknown.

Semi-Markov control processes with non-compact action spaces and discontinuous costs

Anna Jaśkiewicz (2009)

Applicationes Mathematicae

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We establish the average cost optimality equation and show the existence of an (ε-)optimal stationary policy for semi-Markov control processes without compactness and continuity assumptions. The only condition we impose on the model is the V-geometric ergodicity of the embedded Markov chain governed by a stationary policy.