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A Subsampling Line-Search Method with Second-Order Results. (arXiv:1810.07211v1 [math.OC])
来源于:arXiv
In many contemporary optimization problems, such as hyperparameter tuning for
deep learning architectures, it is computationally challenging or even
infeasible to evaluate an entire function or its derivatives. This necessitates
the use of stochastic algorithms that sample problem data, which can jeopardize
the guarantees classically obtained through globalization techniques via a
trust region or a line search. Using subsampled function values is particularly
challenging for the latter strategy, that relies upon multiple evaluations. On
top of that all, there has been an increasing interest for nonconvex
formulations of data-related problems. For such instances, one aims at
developing methods that converge to second-order stationary points, which is
particularly delicate to ensure when one only accesses subsampled
approximations of the objective and its derivatives.
This paper contributes to this rapidly expanding field by presenting a
stochastic algorithm based on negative curvature a 查看全文>>