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Entropy 2015, 17(10), 7266-7297; doi:10.3390/e17107266

Quantifying Emergent Behavior of Autonomous Robots

1
IST Austria, Am Campus 1, 3400 Klosterneuburg, Austria
2
Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, 04103 Leipzig, Germany
*
Author to whom correspondence should be addressed.
Academic Editor: Kevin H. Knuth
Received: 29 June 2015 / Revised: 6 October 2015 / Accepted: 12 October 2015 / Published: 23 October 2015
(This article belongs to the Special Issue Information Theoretic Incentives for Cognitive Systems)
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Abstract

Quantifying behaviors of robots which were generated autonomously from task-independent objective functions is an important prerequisite for objective comparisons of algorithms and movements of animals. The temporal sequence of such a behavior can be considered as a time series and hence complexity measures developed for time series are natural candidates for its quantification. The predictive information and the excess entropy are such complexity measures. They measure the amount of information the past contains about the future and thus quantify the nonrandom structure in the temporal sequence. However, when using these measures for systems with continuous states one has to deal with the fact that their values will depend on the resolution with which the systems states are observed. For deterministic systems both measures will diverge with increasing resolution. We therefore propose a new decomposition of the excess entropy in resolution dependent and resolution independent parts and discuss how they depend on the dimensionality of the dynamics, correlations and the noise level. For the practical estimation we propose to use estimates based on the correlation integral instead of the direct estimation of the mutual information based on next neighbor statistics because the latter allows less control of the scale dependencies. Using our algorithm we are able to show how autonomous learning generates behavior of increasing complexity with increasing learning duration. View Full-Text
Keywords: excess entropy; mutual information; predictive information; quantification; autonomous robots; behavior; correlation integral excess entropy; mutual information; predictive information; quantification; autonomous robots; behavior; correlation integral
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Martius, G.; Olbrich, E. Quantifying Emergent Behavior of Autonomous Robots. Entropy 2015, 17, 7266-7297.

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