Quasi-Newton Methods: A New Direction

2012

Conference Paper

ei

ps

pn

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.

@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},
  doi = {},
  url = {http://www.is.tuebingen.mpg.de/fileadmin/user_upload/files/publications/2012/Hennig_Kiefel_ICML2012.pdf},
  month_numeric = {7}
}