Information Driven Self-Organization of Complex Robotic Behaviors

Abstract

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.

On the Cross-Disciplinary Nature of Guided Self-Organisation

“…Polani 2009;Prokopenko et al 2009;Martius et al 2013), • theory of computation, e.g. (Lizier et al 2008b;Crutchfield 2009;Egri-Nagy and Nehaniv 2011;Dini et al 2013), • dynamical systems, e.g.…”

The Fisher Information as a Neural Guiding Principle for Independent Component Analysis

“…Principles such as maximizing the output entropy of a system to improve the representational richness of the code [19], maximal information transmission for signal separation and deconvolution in networks [33] or maximal predictive information within the sensorimotor loop as a guiding principle to generate behavior [34], have proven successful in the past in both generating new approaches to learning and plasticity and in furthering the understanding of already available rules, integrating them into a broader context by formulating them in terms of a guiding principle [10].…”

On the Role of Embodiment for Self-Organizing Robots: Behavior As Broken Symmetry

“…In recent work, the so called predictive information (PI) was introduced as a general objective function for SO (Ay et al , 2012Zahedi et al 2010;Martius et al 2013). By maximizing the PI, a general learning rule for the synaptic strengths of a neural controller network was derived on the basis of such an Infomax principle.…”

“…In the applications, the learning rate η may be large such that the low complexity of the model is compensated by a fast adaptation process. The learning rule for the controller, given in (Martius et al 2013), was derived from maximization of the predictive information. Based on that, we postulate a new unsupervised learning rule (ULR) which will not be derived here but considered as intuitively grounded by the discussion in Sect.…”

“…There are several approaches into that direction based on formulating objective functions (OFs) for SO. In recent years, several such OFs have been proposed, ranging from the maximization of predictive information (Ay et al , 2012Martius et al 2013) or empowerment (Klyubin et al 2005(Klyubin et al , 2007Anthony et al 2009;Jung et al 2012), to the minimization of free energy (Friston 2010;Friston et al 2012;Friston and Stephan 2007;Friston 2012) or the so called time-loop error in the homeokinesis approach (Der 2001;Der and Liebscher 2002;Der and Martius 2012), see also (Prokopenko 2008(Prokopenko , 2009Prokopenko et al 2009) for more details on how to organize SO. Given an objective function, the optimization process can be translated into a learning rule that is driving the SO process.…”