Notice
Reversible Markov decision processes
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Descriptif
A Markov decision process is called reversible if for every stationary Markov control strategy the resulting Markov chain is reversible. In view of their relevance in applications such as Markov Chain Monte Carlo algorithms, such reversible Markov decision process seem to be of interest to study in their own right. We characterize all discrete time reversible Markov decision processes with finite state and action spaces, generalizing earlier work of Cogill and Peng. We discuss how the policy iteration algorithm to find an optimal stationary Markov control strategy is considerably simplified for reversible Markov decision processes. The potential to apply powerful tools from the study of reversible Markov chains, such as the Poisson gas of Markovian loops and the Gaussian free field, will also be discussed.
Thème
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