Cross Apprenticeship Learning Framework: Properties and Solution Approaches

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 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. We identify conditions under which an agent prefers using the policy obtained from CAL over the traditional apprenticeship learning. Since the CAL 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.