Abstract
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.
Highlights
The goal of this article is to provide a framework that allows us to determine the complexity of a control architecture in accordance with the cheap design principle from embodied artificial intelligence [1, 2]
We present a detailed quantitative case study for policy models defined in terms of conditional restricted Boltzmann machines
We introduce the notions of embodied behavior dimension and embodied universal approximation, which quantify the effective dimension of a system that is subject to sensorimotor constraints and formalize the minimal control paradigm of cheap design in the context of the sensorimotor loop
Summary
The goal of this article is to provide a framework that allows us to determine the complexity of a control architecture in accordance with the cheap design principle from embodied artificial intelligence [1, 2]. Cheap design in this context refers to the relatively low complexity of the brain or controller in comparison with the complexity of an observed behavior. Braitenberg discusses several artificial creatures with simple wirings between sensors and actuators He describes how these systems produce a behavior that an external observer would classify as complex if the internal wirings were not revealed. Sol et al [6] have studied various species and the affected brain regions and point out that the reduced brain sizes could be a direct result from the need to reduce energetic, metabolic and cognitive costs for migrating birds
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