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Journal Article

Quasi-Newton Methods: A New Direction

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Hennig,  P
Dept. Empirical Inference, Max Planck Institute for Intelligent Systems, Max Planck Society;

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Kiefel,  M
Dept. Empirical Inference, Max Planck Institute for Intelligent Systems, Max Planck Society;

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Citation

Hennig, P., & Kiefel, M. (2013). Quasi-Newton Methods: A New Direction. Journal of Machine Learning Research, 14, 843-865.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-B80A-3
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 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.