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<p>The present work proposes an approximating scheme to compute approximate solutions for a class of average cost Markov decision processes with unbounded costs and weakly continuous kernel. The approximations rely on function approximating schemes that can be represented as positive linear operators that gives exact representation to the constant functions. This allows to see the approximated model as a perturbation of the original model and to derive performance bounds for the approximate optimal stationary policies among other things. The bounds are given in terms of the primitive data of the model and the accuracy of the function approximating scheme that is used. It is assumed that the model satisfies a growth condition, a contraction property expressed as a Lyapuov condition and some standard continuity/compactness conditions.</p>

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Approximations with Performance Bounds for a Class of Average Cost Markov Decision Processes with Weakly Continuous Kernel and Unbounded Cost Function

  • 期刊论文

  • 发表日期：

    2026年5月2日

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  • Mauricio Castro-Enríquez,
  • Óscar Vega-Amaya,
  • Fernando Luque-Vásquez

摘要

The present work proposes an approximating scheme to compute approximate solutions for a class of average cost Markov decision processes with unbounded costs and weakly continuous kernel. The approximations rely on function approximating schemes that can be represented as positive linear operators that gives exact representation to the constant functions. This allows to see the approximated model as a perturbation of the original model and to derive performance bounds for the approximate optimal stationary policies among other things. The bounds are given in terms of the primitive data of the model and the accuracy of the function approximating scheme that is used. It is assumed that the model satisfies a growth condition, a contraction property expressed as a Lyapuov condition and some standard continuity/compactness conditions.