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• W13173889 abstract "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 $mathcal{M}$ and a distribution δ goal, whether there exists a (history-dependent randomized) policy π ensuring that the steady-state distribution of $mathcal{M}$ under π is exactly δ 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 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." @default.
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• W13173889 date "2013-01-01" @default.
• W13173889 modified "2023-10-06" @default.
• W13173889 title "The Steady-State Control Problem for Markov Decision Processes" @default.
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• W13173889 doi "https://doi.org/10.1007/978-3-642-40196-1_26" @default.
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