  In learning from demonstrations, many generative models of trajectories make
simplifying assumptions of independence. Correctness is sacrificed in the name
of tractability and speed of the learning phase.
  The ignored dependencies, which often are the kinematic and dynamic
constraints of the system, are then only restored when synthesizing the motion,
which introduces possibly heavy distortions.
  In this work, we propose to use those approximate trajectory distributions as
close-to-optimal discriminators in the popular generative adversarial framework
to stabilize and accelerate the learning procedure.
  The two problems of adaptability and robustness are addressed with our
method.
  In order to adapt the motions to varying contexts, we propose to use a
product of Gaussian policies defined in several parametrized task spaces.
Robustness to perturbations and varying dynamics is ensured with the use of
stochastic gradient descent and ensemble methods to learn the stochastic
dynamics. Two experiments are performed on a 7-DoF manipulator to validate the
approach.
