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S Akshay, N. Bertrand, Haddad S, L. Hélouet. The steady-state control problem for Markov decision processes. In 10th International Conference on Quantitative Evaluation of SysTems (QEST'13), LNCS, Volume 8054, Pages 390-304, Buenos Aires, Argentina, August 2013.

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This paper addresses a control problem for probabilistic models in the setting of Markov decision processes (MDP). We are interested in the steady-state control problem which asks, given an ergodic MDP M and a distribution \delta, whether there exists a (history-dependent randomized) policy \pi ensuring that the steady-state distribution of M under \pi is exactly \delta. 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 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


Nathalie Bertrand http://www.irisa.fr/prive/nbertran/
Loic Hélouet http://people.irisa.fr/Loic.Helouet/

BibTex Reference

   Author = {Akshay, S and Bertrand, N. and S, Haddad and Hélouet, L.},
   Title = {The steady-state control problem for Markov decision processes},
   BookTitle = {10th International Conference on Quantitative Evaluation of SysTems (QEST'13)},
   Volume = {8054},
   Pages = {390--304},
   Series = {LNCS},
   Address = {Buenos Aires, Argentina},
   Month = {August},
   Year = {2013}

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