  Apprenticeship learning is a framework in which an agent learns a policy to
perform a given task in an environment using example trajectories provided by
an expert. In the real world, one might have access to expert trajectories in
different environments where the system dynamics is different while the
learning task is the same. For such scenarios, two types of learning objectives
can be defined. One where the learned policy performs very well in one specific
environment and another when it performs well across all environments. To
balance these two objectives in a principled way, our work presents the cross
apprenticeship learning (CAL) framework. This consists of an optimization
problem where an optimal policy for each environment is sought while ensuring
that all policies remain close to each other. This nearness is facilitated by
one tuning parameter in the optimization problem. We derive properties of the
optimizers of the problem as the tuning parameter varies. Since the problem is
nonconvex, we provide a convex outer approximation. Finally, we demonstrate the
attributes of our framework in the context of a navigation task in a windy
gridworld environment.
