A Theory of Cheap Control in Embodied Systems
This work addresses the challenge of reducing computational complexity in control systems for embodied agents, offering a novel theoretical framework with practical implications, though it is incremental in building on universal approximation concepts.
The authors tackled the problem of designing efficient control architectures for embodied agents by introducing a framework for cheap universal approximation that exploits embodiment, showing that it requires drastically fewer parameters than classical non-embodied methods, with a case study using conditional restricted Boltzmann machines and experimental validation on a six-legged walking machine confirming tight controller complexity.
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. Keywords: cheap design, embodiment, sensorimotor loop, universal approximation, conditional restricted Boltzmann machine