MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

A Theory of Cheap Control in Embodied Systems

Guido Montúfar, Keyan Ghazi-Zahedi and Nihat Ay


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.

MSC Codes:
68T05, 60K99
02.50.Cw, 07.05.Mh
universal approximation, cheap design, embodiment, sensorimotor loop, conditional restricted Boltzmann machine

Related publications

2015 Journal Open Access
Guido Montúfar, Keyan Ghazi-Zahedi and Nihat Ay

A theory of cheap control in embodied systems

In: PLoS computational biology, 11 (2015) 9, e1004427