  We consider the Adaptive Regularization with Cubics approach for solving
nonconvex optimization problems and propose a new variant based on inexact
Hessian information chosen dynamically. The theoretical analysis of the
proposed procedure is given. The key property of ARC framework, constituted by
optimal worst-case function/derivative evaluation bounds for first- and
second-order critical point, is guaranteed. Application to large-scale
finite-sum minimization based on subsampled Hessian is discussed and analyzed
in both a deterministic and probabilistic manner and equipped with numerical
experiments on synthetic and real datasets.
