Abstract

Motivation: Classical definitions of information, such as the Shannon information, are designed for open loop systems because they define information on a channel which has an input and an output. The main motivation of this paper is to present a closed loop information measure which is compatible with constructivist thinking. Design: Our information measure for a closed loop system reflects how additional sensor inputs are utilised to establish additional sensor-motor loops during learning. Our information measure is based on the assumption that it is not optimal to stay reactive and that it is beneficial to become proactive through increased learning about the environment. Consequently our information measure gauges the utilisation of new sensor inputs to generate anticipatory actions. We call this information measure "predictive information" (PI). Findings: Our PI is zero if the organism uses only its reflex reactions. It grows when the organism is able to use other sensor inputs to preempt reflex reactions and is able to replace reflexes by anticipatory reactions. This has been demonstrated with a real robot that had to learn to avoid obstacles. Conclusion: PI is a new measure which is able to quantify anticipatory learning and, in contrast to the Shannon information, is calculated only at the inputs of an agent. This information measure has been successfully applied to a simple robot task but its application is neither limited to a certain task nor to a certain learning rule.