Learning Dynamics: System Identification for Perceptually Challenged Agents

From the perspective of an agent, the input/output behavior of the environment in which it is embedded can be described as a dynamical system. Inputs correspond to the actions executable by the agent in making transitions between states of the environment. Outputs correspond to the perceptual information available to the agent in particular states of the environment. We view dynamical system identiication as inference of deterministic nite-state automata from sequences of input/output pairs. The agent can innuence the sequence of input/output pairs it is presented by pursuing a strategy for exploring the environment. We identify two sorts of perceptual errors: errors in perceiving the output of a state and errors in perceiving the inputs actually carried out in making a transition from one state to another. We present eecient, high-probability learning algorithms for a number of system identiication problems involving such errors. We also present the results of empirical investigations applying these algorithms to learning spatial representations.