Dynamical System Embedding for Efficient Intrinsically Motivated Artificial Agents

Mutual Information between agent Actions and environment States (MIAS) quantifies the influence of agent on its environment. Recently, it was found that intrinsic motivation in artificial agents emerges from the maximization of MIAS. For example, empowerment is an information-theoretic approach to intrinsic motivation, which has been shown to solve a broad range of standard RL benchmark problems. The estimation of empowerment for arbitrary dynamics is a challenging problem because it relies on the estimation of MIAS. Existing approaches rely on sampling, which have formal limitations, requiring exponentially many samples. In this work, we develop a novel approach for the estimation of empowerment in unknown arbitrary dynamics from visual stimulus only, without sampling for the estimation of MIAS. The core idea is to represent the relation between action sequences and future states by a stochastic dynamical system in latent space, which admits an efficient estimation of MIAS by the ``Water-Filling" algorithm from information theory. We construct this embedding with deep neural networks trained on a novel objective function and demonstrate our approach by numerical simulations of non-linear continuous-time dynamical systems. We show that the designed embedding preserves information-theoretic properties of the original dynamics, and enables us to solve the standard AI benchmark problems.