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Sample path average optimality of Markov control processes with strictly unbounded cost

Oscar Vega-Amaya — 1999

Applicationes Mathematicae

We study the existence of sample path average cost (SPAC-) optimal policies for Markov control processes on Borel spaces with strictly unbounded costs, i.e., costs that grow without bound on the complement of compact subsets. Assuming only that the cost function is lower semicontinuous and that the transition law is weakly continuous, we show the existence of a relaxed policy with 'minimal' expected average cost and that the optimal average cost is the limit of discounted programs. Moreover, we...

Sample-path average cost optimality for semi-Markov control processes on Borel spaces: unbounded costs and mean holding times

Oscar Vega-AmayaFernando Luque-Vásquez — 2000

Applicationes Mathematicae

We deal with semi-Markov control processes (SMCPs) on Borel spaces with unbounded cost and mean holding time. Under suitable growth conditions on the cost function and the mean holding time, together with stability properties of the embedded Markov chains, we show the equivalence of several average cost criteria as well as the existence of stationary optimal policies with respect to each of these criteria.

A perturbation approach to approximate value iteration for average cost Markov decision processes with Borel spaces and bounded costs

Óscar Vega-AmayaJoaquín López-Borbón — 2019

Kybernetika

The present paper studies the approximate value iteration (AVI) algorithm for the average cost criterion with bounded costs and Borel spaces. It is shown the convergence of the algorithm and provided a performance bound assuming that the model satisfies a standard continuity-compactness assumption and a uniform ergodicity condition. This is done for the class of approximation procedures that can be represented by linear positive operators which give exact representation of constant functions and...

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