Predictive information and explorative behavior of autonomous robots

Measures of complexity are of immediate interest for the field of autonomous robots both as a means to classify the behavior and as an objective function for the autonomous development of robot behavior. In the present paper we consider predictive information in sensor space as a measure for the behavioral complexity of a two-wheel embodied robot moving in a rectangular arena with several obstacles. The mutual information (MI) between past and future sensor values is found empirically to have a maximum for a behavior which is both explorative and sensitive to the environment. This makes predictive information a prospective candidate as an objective function for the autonomous development of such behaviors. We derive theoretical expressions for the MI in order to obtain an explicit update rule for the gradient ascent dynamics. Interestingly, in the case of a linear or linearized model of the sensorimotor dynamics the structure of the learning rule derived depends only on the dynamical properties while the value of the MI influences only the learning rate. In this way the problem of the prohibitively large sampling times for information theoretic measures can be circumvented. This result can be generalized and may help to derive explicit learning rules from complexity theoretic measures.