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  Quasi-Newton Methods: A New Direction

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

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http://jmlr.org/papers/v14/hennig13a.html (Publisher version)
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Hennig, P1, Author              
Kiefel, M1, Author              
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1Dept. Empirical Inference, Max Planck Institute for Intelligent Systems, Max Planck Society, DE, ou_1497647              

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 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.

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 Dates: 2013-03
 Publication Status: Published in print
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 Identifiers: BibTex Citekey: HennigK2012_2
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Title: Journal of Machine Learning Research
Source Genre: Journal
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Pages: - Volume / Issue: 14 Sequence Number: - Start / End Page: 843 - 865 Identifier: -