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A Theory of Cheap Control in Embodied Systems.

Montúfar G, Ghazi-Zahedi K, Ay N - PLoS Comput. Biol. (2015)

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany.

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.

No MeSH data available.


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Sensorimotor loop.
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pcbi.1004427.g001: Sensorimotor loop.

Mentions: The sensorimotor loop (SML) [21, 22] is described by a type of partially observable Markov decision process (POMDP) where an embodied agent chooses actions based on noisy partial observations of its environment. An illustration of this causal structure is given in Fig 1. We aim at optimizing the design of policy models for controlling these processes. One aspect of the optimal design problem is addressed by working out the optimal complexity of the policy model. In particular, we are interested in the minimal number of units or parameters needed in order to obtain an artificial neural network that can represent or approximate a desired set of behaviors. A first step towards resolving this problem is to address the minimal size of a universal approximator of policies. In realistic scenarios, universal approximation is out of question, since it demands an enormous number of parameters, many more than actually needed. In this paper we reconsider the universal approximation problem by exploiting embodiment constraints and restrictions in the desired behavioral patterns.


A Theory of Cheap Control in Embodied Systems.

Montúfar G, Ghazi-Zahedi K, Ay N - PLoS Comput. Biol. (2015)

Sensorimotor loop.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4556690&req=5

pcbi.1004427.g001: Sensorimotor loop.
Mentions: The sensorimotor loop (SML) [21, 22] is described by a type of partially observable Markov decision process (POMDP) where an embodied agent chooses actions based on noisy partial observations of its environment. An illustration of this causal structure is given in Fig 1. We aim at optimizing the design of policy models for controlling these processes. One aspect of the optimal design problem is addressed by working out the optimal complexity of the policy model. In particular, we are interested in the minimal number of units or parameters needed in order to obtain an artificial neural network that can represent or approximate a desired set of behaviors. A first step towards resolving this problem is to address the minimal size of a universal approximator of policies. In realistic scenarios, universal approximation is out of question, since it demands an enormous number of parameters, many more than actually needed. In this paper we reconsider the universal approximation problem by exploiting embodiment constraints and restrictions in the desired behavioral patterns.

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany.

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.

No MeSH data available.


Related in: MedlinePlus