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We consider the Adaptive Regularization with Cubics approach for solvingnonconvex optimization problems and propose a new variant based on inexactHessian information chosen dynamically. The theoretical analysis of theproposed procedure is given. The key property of ARC framework, constituted byoptimal worst-case function/derivative evaluation bounds for first- andsecond-order critical point, is guaranteed. Application to large-scalefinite-sum minimization based on subsampled Hessian is discussed and analyzedin both a deterministic and probabilistic manner and equipped with numericalexperiments on synthetic and real datasets.

Adaptive Cubic Regularization Methods with Dynamic Inexact Hessian Information and Applications to Finite-Sum Minimization