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We present a stochastic optimization method that uses a fourth-order regularized model to find local minima of smooth and potentially non-convex objective functions with a finite-sum structure.
Fast exact multiplication by the hessian
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Introductory lectures on convex optimization. applied optimization, vol. 87, 2004
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Concentration inequalities for sampling without replacement
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Peng Xu, Farbod Roosta-Khorasani, and Michael W Mahoney · 2017
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Accelerated methods for nonconvex optimization
Yair Carmon, John C Duchi, Oliver Hinder, and Aaron Sidford · 2018
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Second-order optimality and beyond: Characterization and evaluation complexity in convexly constrained nonlinear optimization
Coralia Cartis, Nick IM Gould, and Philippe L Toint · 2018
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Stochastic variance-reduced cubic regularization for nonconvex optimization
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First-order stochastic algorithms for escaping from saddle points in almost linear time
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