  In this paper, we are interested in optimal decisions in a partially
observable Markov universe. Our viewpoint departs from the dynamic programming
viewpoint: we are directly approximating an optimal strategic tree depending on
the observation. This approximation is made by means of a parameterized
probabilistic law. In this paper, a particular family of hidden Markov models,
with input and output, is considered as a learning framework. A method for
optimizing the parameters of these HMMs is proposed and applied. This
optimization method is based on the cross-entropic principle.
