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A group-theoretic approach to formalizing bootstrapping problems

Censi, Andrea and Murray, Richard M. (2011) A group-theoretic approach to formalizing bootstrapping problems. Caltech , Pasadena, CA. (Unpublished) http://resolver.caltech.edu/CaltechCDSTR:2011.005

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Abstract

The bootstrapping problem consists in designing agents that learn a model of themselves and the world, and utilize it to achieve useful tasks. It is different from other learning problems as the agent starts with uninterpreted observations and commands, and with minimal prior information about the world. In this paper, we give a mathematical formalization of this aspect of the problem. We argue that the vague constraint of having "no prior information" can be recast as a precise algebraic condition on the agent: that its behavior is invariant to particular classes of nuisances on the world, which we show can be well represented by actions of groups (diffeomorphisms, permutations, linear transformations) on observations and commands. We then introduce the class of bilinear gradient dynamics sensors (BGDS) as a candidate for learning generic robotic sensorimotor cascades. We show how framing the problem as rejection of group nuisances allows a compact and modular analysis of typical preprocessing stages, such as learning the topology of the sensors. We demonstrate learning and using such models on real-world range-finder and camera data from publicly available datasets.


Item Type:Report or Paper (Technical Report)
Group:Control and Dynamical Systems Technical Reports
Record Number:CaltechCDSTR:2011.005
Persistent URL:http://resolver.caltech.edu/CaltechCDSTR:2011.005
Usage Policy:You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.
ID Code:28145
Collection:CaltechCDSTR
Deposited By: Imported from CaltechCDSTR
Deposited On:18 Apr 2011
Last Modified:26 Dec 2012 14:31

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