On discovery and learning of models with predictive representations of state for agents with continuous actions and observations

Models of agent-environment interaction that use predictive state representations (PSRs) have mainly focused on the case of discrete observations and actions. The theory of discrete PSRs uses an elegant construct called the system dynamics matrix and derives the notion of predictive state as a sufficient statistic via the rank of the matrix. With continuous observations and actions, such a matrix and its rank no longer exist. In this paper, we show how to define an analogous construct for the continuous case, called the system dynamics distributions, and use information theoretic notions to define a sufficient statistic and thus state. Given this new construct, we use kernel density estimation to learn approximate system dynamics distributions from data, and use information-theoretic tools to derive algorithms for discovery of state and learning of model parameters. We illustrate our new modeling method on two example problems.