Learning the Difference between Partially Observable Dynamical Systems

We propose a new approach for estimating the difference between two partially observable dynamical systems. We assume that one can interact with the systems by performing actions and receiving observations. The key idea is to define a Markov Decision Process (MDP) based on the systems to be compared, in such a way that the optimal value of the MDP initial state can be interpreted as a divergence (or dissimilarity) between the systems. This dissimilarity can then be estimated by reinforcement learning methods. Moreover, the optimal policy will contain information about the actions which most distinguish the systems. Empirical results show that this approach is useful in detecting both big and small differences, as well as in comparing systems with different internal structure.