Autonomous Learning Conference Paper 2018

Learning equations for extrapolation and control

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We present an approach to identify concise equations from data using a shallow neural network approach. In contrast to ordinary black-box regression, this approach allows understanding functional relations and generalizing them from observed data to unseen parts of the parameter space. We show how to extend the class of learnable equations for a recently proposed equation learning network to include divisions, and we improve the learning and model selection strategy to be useful for challenging real-world data. For systems governed by analytical expressions, our method can in many cases identify the true underlying equation and extrapolate to unseen domains. We demonstrate its effectiveness by experiments on a cart-pendulum system, where only 2 random rollouts are required to learn the forward dynamics and successfully achieve the swing-up task.

Author(s): Subham S. Sahoo and Christoph H. Lampert and Georg Martius
Book Title: Proc. \35th International Conference on Machine Learning, ICML 2018, Stockholm, Sweden, 2018
Volume: 80
Pages: 4442--4450
Year: 2018
Editors: Dy, Jennifer and Krause, Andreas
Publisher: {PMLR}
Project(s):
Bibtex Type: Conference Paper (inproceedings)
URL: http://proceedings.mlr.press/v80/sahoo18a.html
Electronic Archiving: grant_archive
How Published: http://proceedings.mlr.press/v80/sahoo18a/sahoo18a.pdf
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BibTex

@inproceedings{SahooLampertMartius2018:EQLDiv,
  title = {Learning equations for extrapolation and control},
  booktitle = {Proc. \textbackslash 35th International Conference on Machine Learning, {ICML} 2018, Stockholm, Sweden, 2018},
  abstract = {We present an approach to identify concise equations from data using a
  shallow neural network approach. In contrast to ordinary black-box
  regression, this approach allows understanding functional relations and
  generalizing them from observed data to unseen parts of the parameter
  space. We show how to extend the class of learnable equations for a
  recently proposed equation learning network to include divisions, and we
  improve the learning and model selection strategy to be useful for
  challenging real-world data. For systems governed by analytical
  expressions, our method can in many cases identify the true underlying
  equation and extrapolate to unseen domains. We demonstrate its
  effectiveness by experiments on a cart-pendulum system, where only 2
  random rollouts are required to learn the forward dynamics and
  successfully achieve the swing-up task.},
  volume = {80},
  pages = {4442--4450},
  howpublished = {http://proceedings.mlr.press/v80/sahoo18a/sahoo18a.pdf},
  editors = {Dy, Jennifer and Krause, Andreas},
  publisher = {{PMLR}},
  year = {2018},
  slug = {sahoolampertmartius2018-eqldiv},
  author = {Sahoo, Subham S. and Lampert, Christoph H. and Martius, Georg},
  url = {http://proceedings.mlr.press/v80/sahoo18a.html}
}