Quasi-Newton Methods: A New Direction

Philipp Hennig; Martin Kiefel

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arXiv · 1206.4602

Quasi-Newton Methods: A New Direction

Philipp Hennig·Martin Kiefel

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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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Philipp Hennig, Martin Kiefel. 2012-06-18. Quasi-Newton Methods: A New Direction. https://arxiv.org/abs/1206.4602

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