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Quasi-Newton Methods: A New Direction

2012

Conference Paper

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Four decades after their invention, quasi- Newton methods are still state of the art in unconstrained numerical optimization. Although not usually interpreted thus, these are learning algorithms that fit a local quadratic approximation to the objective function. We show that many, including the most popular, quasi-Newton methods can be interpreted as approximations of Bayesian linear regression under varying prior assumptions. This new notion elucidates some shortcomings of classical algorithms, and lights the way to a novel nonparametric quasi-Newton method, which is able to make more efficient use of available information at computational cost similar to its predecessors.

Author(s): Hennig, Philipp and Kiefel, Martin
Book Title: Proceedings of the 29th International Conference on Machine Learning
Pages: 25--32
Year: 2012
Month: July

Series: ICML '12
Editors: John Langford and Joelle Pineau
Publisher: Omnipress

Department(s): Empirical Inference, Perceiving Systems, Probabilistic Numerics
Research Project(s): Probabilistic Methods for Nonlinear Optimization
Probabilistic Numerics
Bibtex Type: Conference Paper (inproceedings)
Paper Type: Conference

Event Name: ICML 2012
Event Place: Edinburgh, Scotland, GB

Address: New York, NY, USA
URL: http://www.is.tuebingen.mpg.de/fileadmin/user_upload/files/publications/2012/Hennig_Kiefel_ICML2012.pdf

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BibTex

@inproceedings{optimization,
  title = {Quasi-Newton Methods: A New Direction},
  author = {Hennig, Philipp and Kiefel, Martin},
  booktitle = {Proceedings of the 29th International Conference on Machine Learning},
  pages = {25--32},
  series = {ICML '12},
  editors = {John Langford and Joelle Pineau},
  publisher = {Omnipress},
  address = {New York, NY, USA},
  month = jul,
  year = {2012},
  url = {http://www.is.tuebingen.mpg.de/fileadmin/user_upload/files/publications/2012/Hennig_Kiefel_ICML2012.pdf},
  month_numeric = {7}
}