The steady-state control problem for Markov decision processes - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Communication Dans Un Congrès Année : 2013

The steady-state control problem for Markov decision processes

Résumé

This paper addresses a control problem for probabilistic models in the setting of Markov decision processes (\MDP). We are interested in the \emph{steady-state control problem} which asks, given an ergodic \MDP\ $\mathcal M$ and a distribution $\delta_{goal}$, whether there exists a (history-dependent randomized) policy $\pi$ ensuring that the steady-state distribution of $\mathcal M$ under $\pi$ is exactly $\delta_{goal}$. We first show that stationary randomized policies suffice to achieve a given steady-state distribution. Then we infer that the steady-state control problem is decidable for \MDP, and can be represented as a linear program which is solvable in PTIME. This decidability result extends to labeled \MDP\ (\LMDP) where the objective is a steady-state distribution on labels carried by the states, and we provide a PSPACE algorithm. We also show that a related \emph{steady-state language inclusion problem} is decidable in EXPTIME for \LMDP. Finally, we prove that if we consider \MDP\ under partial observation (\POMDP), the steady-state control problem becomes undecidable.
Fichier principal
Vignette du fichier
Qest_paper_29.pdf (170.4 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00879355 , version 1 (02-11-2013)

Identifiants

  • HAL Id : hal-00879355 , version 1

Citer

Sundararaman Akshay, Nathalie Bertrand, Serge Haddad, Loïc Hélouët. The steady-state control problem for Markov decision processes. Qest 2013, Sep 2013, Buenos Aires, Argentina. pp.290-304. ⟨hal-00879355⟩
408 Consultations
267 Téléchargements

Partager

Gmail Facebook X LinkedIn More