Approximation of average cost Markov decision processes using empirical distributions and concentration inequalities
DUFOUR, François
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]
DUFOUR, François
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]
< Leer menos
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]
Idioma
en
Article de revue
Este ítem está publicado en
Stochastics: An International Journal of Probability and Stochastic Processes. 2015, vol. 87, n° 2, p. 273 - 307
Taylor & Francis: STM, Behavioural Science and Public Health Titles
Resumen en inglés
We consider a discrete-time Markov decision process with Borel state and action spaces, and possibly unbounded cost function. We assume that the Markov transition kernel is absolutely continuous with respect to some ...Leer más >
We consider a discrete-time Markov decision process with Borel state and action spaces, and possibly unbounded cost function. We assume that the Markov transition kernel is absolutely continuous with respect to some probability measure . By replacing this probability measure with its empirical distribution for a sample of size n, we obtain a finite state space control problem, which is used to provide an approximation of the optimal value and an optimal policy of the original control model. We impose Lipschitz continuity properties on the control model and its associated density functions. We measure the accuracy of the approximation of the optimal value and an optimal policy by means of a non-asymptotic concentration inequality based on the 1-Wasserstein distance between and . Obtaining numerically the solution of the approximating control model is discussed and an application to an inventory management problem is presented.< Leer menos
Palabras clave en inglés
Wasserstein distance
Concentration inequalities
Approximation of the optimal value and an optimal policy
Long-run average cost
Markov decision processes
Orígen
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