Sample-path optimality and variance-minimization of average cost Markov control processes

Onésimo Hernández-Lerma; Oscar Vega-Amaya; Guadalupe Carrasco

doi:10.1137/S0363012998340673

Sample-path optimality and variance-minimization of average cost Markov control processes

Onésimo Hernández-Lerma, Oscar Vega-Amaya, Guadalupe Carrasco

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Abstract

This paper studies several average-cost criteria for Markov control processes on Borel spaces with possibly unbounded costs. Under suitable hypotheses we show (i) the existence of a sample-path average cost (SPAC-) optimal stationary policy; (ii) a stationary policy is SPAC-optimal if and only if it is expected average cost (EAC-) optimal; and (iii) within the class of stationary SPAC-optimal (equivalently, EAC-optimal) policies there exists one with a minimal limiting average variance.

Original language	English
Pages (from-to)	79-93
Number of pages	15
Journal	SIAM Journal on Control and Optimization
Volume	38
Issue number	1
DOIs	https://doi.org/10.1137/S0363012998340673
State	Published - 1999

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AB - This paper studies several average-cost criteria for Markov control processes on Borel spaces with possibly unbounded costs. Under suitable hypotheses we show (i) the existence of a sample-path average cost (SPAC-) optimal stationary policy; (ii) a stationary policy is SPAC-optimal if and only if it is expected average cost (EAC-) optimal; and (iii) within the class of stationary SPAC-optimal (equivalently, EAC-optimal) policies there exists one with a minimal limiting average variance.

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Sample-path optimality and variance-minimization of average cost Markov control processes

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