An Approach for Determining the Optimal Strategies for an Average Markov Decision Problem with Finite State and Action Spaces
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519.217 (12)
Probabilitate. Statistică matematică (48)
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Buletinul Academiei de Ştiinţe a Moldovei. Matematica
Numărul 1(86) / 2018 / ISSN 1024-7696

An Approach for Determining the Optimal Strategies for an Average Markov Decision Problem with Finite State and Action Spaces


CZU: 519.217
MSC 2010: 90C15, 90C40.
Pag. 34-49

Lozovanu Dmitrii1, Pickl Stefan2
 
1 Institute of Mathematics and Computer Science of the Academy of Sciences of Moldova,
2 Institut für Theoretische Informatik, Mathematik und Operations Research
 
Disponibil în IBN: 26 iulie 2018


Rezumat

The average reward Markov decision problem with finite state and action spaces is considered and an approach for determining the optimal pure and mixed stationary strategies for this problem is proposed. We show that the considered problem can be formulated in terms of stationary strategies where the objective function is quasi-monotonic (i. e. it is quasi-convex and quasi-concave) on the feasible set of stationary strategies. Using such a quasi-monotonic programming model with linear constraints we ground algorithms for determining the optimal pure and mixed stationary strategies for the average Markov decision problem.

Cuvinte-cheie
Markov decision processes, Average optimization criterion, stationary strategies, Optimal strategies.