Abstract.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. PACS

Information theory is a powerful tool to express principles to drive autonomous systems because it is domain invariant and allows for an intuitive interpretation. This paper studies the use of the predictive information (PI), also called excess entropy or effective measure complexity, of the sensorimotor process as a driving force to generate behavior. We study nonlinear and nonstationary systems and introduce the time-local predicting information (TiPI) which allows us to derive exact results together with explicit update rules for the parameters of the controller in the dynamical systems framework. In this way the information principle, formulated at the level of behavior, is translated to the dynamics of the synapses. We underpin our results with a number of case studies with high-dimensional robotic systems. We show the spontaneous cooperativity in a complex physical system with decentralized control. Moreover, a jointly controlled humanoid robot develops a high behavioral variety depending on its physics and the environment it is dynamically embedded into. The behavior can be decomposed into a succession of low-dimensional modes that increasingly explore the behavior space. This is a promising way to avoid the curse of dimensionality which hinders learning systems to scale well.

The neighborhood preservation of self-organizing feature maps like the Kohonen map is an important property which is exploited in many applications. However, if a dimensional conflict arises this property is lost. Various qualitative and quantitative approaches are known for measuring the degree of topology preservation. They are based on using the locations of the synaptic weight vectors. These approaches, however, may fail in case of nonlinear data manifolds. To overcome this problem, in this paper we present an approach which uses what we call the induced receptive fields for determining the degree of topology preservation. We first introduce a precise definition of topology preservation and then propose a tool for measuring it, the topographic function. The topographic function vanishes if and only if the map is topology preserving. We demonstrate the power of this tool for various examples of data manifolds.

This work presents a novel learning method in the context of embodied artificial intelligence and self-organization, which has as few assumptions and restrictions as possible about the world and the underlying model. The learning rule is derived from the principle of maximizing the predictive information in the sensorimotor loop. It is evaluated on robot chains of varying length with individually controlled, non-communicating segments. The comparison of the results shows that maximizing the predictive information per wheel leads to a higher coordinated behavior of the physically connected robots compared to a maximization per robot. Another focus of this paper is the analysis of the effect of the robot chain length on the overall behavior of the robots. It will be shown that longer chains with less capable controllers outperform those of shorter length and more complex controllers. The reason is found and discussed in the information-geometric interpretation of the learning process.