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

arXiv: https://arxiv.org/abs/1808.06239 · HTML: https://mlsanity.com/paper/1808.06239/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Aug 2018.

## Built on by (most cited first, 2 of 2)

- [Extra-Newton: A First Approach to Noise-Adaptive Accelerated Second-Order Methods](https://mlsanity.com/paper/2211.01832/) (2022)
- [Stochastic Optimization for Non-convex Problem with Inexact Hessian Matrix, Gradient, and Function](https://mlsanity.com/paper/2310.11866/) (2023)

## Abstract (arXiv)

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.