A Theory of Cheap Control in Embodied Systems.
We present a framework for designing cheap control architectures of 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 indicate that the controller complexity predicted by our theory is close to the minimal sufficient value, which means that the theory has direct practical implications.
Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany.
Guido
G
Montúfar
Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany.
Keyan
K
Ghazi-Zahedi
Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany; Department of Mathematics and Computer Science, Leipzig University, 04009 Leipzig, Germany; Santa Fe Institute, Santa Fe, New Mexico, United States of America.
Nihat
N
Ay
D005246:Feedback; D008954:Models, Biological; D008959:Models, Neurological; D009038:Motion; D016571:Neural Networks, Computer; D012371:Robotics / Q000379:methods*