A Theory of Cheap Control in Embodied Systems

Guido Montúfar, Keyan Ghazi-Zahedi, and Nihat Ay

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Submission date: 25. Jul. 2014 (revised version: November 2014)
Pages: 29
published in: PLoS computational biology, 11 (2015) 9, art-no. e1004427 
DOI number (of the published article): 10.1371/journal.pcbi.1004427
Bibtex
MSC-Numbers: 68T05, 60K99
PACS-Numbers: 02.50.Cw, 07.05.Mh
Keywords and phrases: universal approximation, cheap design, embodiment, sensorimotor loop, conditional restricted Boltzmann machine
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Abstract:
We present a framework for designing cheap control architectures for embodied agents. Our derivation is guided by the classical problem of universal approximation, whereby we explore the possibility of exploiting the agent's embodiment for a new and more efficient universal approximation of behaviors generated by sensorimotor control. This embodied universal approximation is compared with the classical non-embodied universal approximation. To exemplify our approach, we present a detailed quantitative case study for policy models defined in terms of conditional restricted Boltzmann machines. In contrast to non-embodied universal approximation, which requires an exponential number of parameters, in the embodied setting we are able to generate all possible behaviors with a drastically smaller model, thus obtaining cheap universal approximation. We test and corroborate the theory experimentally with a six-legged walking machine. The experiments show that the sufficient controller complexity predicted by our theory is tight, which means that the theory has direct practical implications.