  Revision of the paper previously entitled "Learning a Machine for the
Decision in a Partially Observable Markov Universe" In this paper, we are
interested in optimal decisions in a partially observable universe. Our
approach is to directly approximate an optimal strategic tree depending on the
observation. This approximation is made by means of a parameterized
probabilistic law. A particular family of hidden Markov models, with input
\emph{and} output, is considered as a model of policy. A method for optimizing
the parameters of these HMMs is proposed and applied. This optimization is
based on the cross-entropic principle for rare events simulation developed by
Rubinstein.
