# Inexact Tensor Methods with Dynamic Accuracies

arXiv: https://arxiv.org/abs/2002.09403 · HTML: https://mlsanity.com/paper/2002.09403/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Feb 2020.

## Built on by (most cited first, 3 of 3)

- [Regularized Newton Method with Global O(1/k2) Convergence](https://mlsanity.com/paper/2112.02089/) (2021)
- [Cubic regularized subspace Newton for non-convex optimization](https://mlsanity.com/paper/2406.16666/) (2024)
- [Second-Order Optimization with Asynchronous Curvature](https://mlsanity.com/paper/2510.15714/) (2025)

## Abstract (arXiv)

In this paper, we study inexact high-order Tensor Methods for solving convex optimization problems with composite objective. At every step of such methods, we use approximate solution of the auxiliary problem, defined by the bound for the residual in function value. We propose two dynamic strategies for choosing the inner accuracy: the first one is decreasing as 1/kp + 1, where p ≥ 1 is the order of the method and k is the iteration counter, and the second approach is using for the inner accuracy the last progress in the target objective. We show that inexact Tensor Methods with these strategies achieve the same global convergence rate as in the error-free case. For the second approach we also establish local superlinear rates (for p ≥ 2), and propose the accelerated scheme. Lastly, we present computational results on a variety of machine learning problems for several methods and different accuracy policies.