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Conference Paper

Quasi-Newton Methods: A New Direction

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons84387

Hennig,  P
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons84384

Kiefel,  M
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Citation

Hennig, P., & Kiefel, M. (2012). Quasi-Newton Methods: A New Direction. In 29th International Conference on Machine Learning (ICML 2012) (pp. 1-8). Madison, WI, USA: International Machine Learning Society.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-B6CA-1
Abstract
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 t 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 ecient use of available information at computational cost similar to its predecessors.