Adaptive Regularized Newton Methods with Inexact Hessian
optimization;second-order methods
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@misc{
shestakov2024adaptive,
title={Adaptive Regularized Newton Methods with Inexact Hessian},
author={Alexander Shestakov and Andrei Semenov and Aleksandr Beznosikov and Alexander Gasnikov and Martin Tak{\'a}{\v{c}} and Dmitry Kamzolov},
year={2024},
url={https://openreview.net/forum?id=rSQb9piM6N}
}
Newton’s Method is the most widespread high-order method, demanding only the gradient and the Hessian of the objective function. However, one of the main disadvantages of Newton's method is its lack of global convergence. There are various ways to deal with it: Cubic Regularization of the Newton Method, Damped Newton Method, Quasi-Newton Methods etc. Another disadvantage is the high iteration cost in modern high dimension problems. In this paper we derive the convergence of Regularization of Newton Method with Bregman divergences for convex, non-convex functions that can be applied with various inexact Hessians. By obtaining global convergence, complexity of iteration stays the same up to logarithmic factor. We show that our theory is validated by multiple experiments, showing competitive performance among other Newton Methods.
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~Alexander_Shestakov1 ~Andrei_Semenov1 ~Aleksandr_Beznosikov1 ~Alexander_Gasnikov1 ~Martin_Takáč1 ~Dmitry_Kamzolov1
Alexander Shestakov Andrei Semenov Aleksandr Beznosikov Alexander Gasnikov Martin Takáč Dmitry Kamzolov
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optimization second-order methods
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shestakov|adaptive_regularized_newton_methods_with_inexact_hessian
optimization
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Adaptive Regularized Newton Methods with Inexact Hessian
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