# Inexact Tensor Methods and Their Application to Stochastic Convex Optimization

arXiv: https://arxiv.org/abs/2012.15636 · HTML: https://mlsanity.com/paper/2012.15636/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Dec 2020.

## Built on by (most cited first, 6 of 6)

- [Unified Convergence Theory of Stochastic and Variance-Reduced Cubic Newton Methods](https://mlsanity.com/paper/2302.11962/) (2023)
- [Improving Stochastic Cubic Newton with Momentum](https://mlsanity.com/paper/2410.19644/) (2024)
- [Cubic regularized subspace Newton for non-convex optimization](https://mlsanity.com/paper/2406.16666/) (2024)
- [Gradient-Normalized Smoothness for Optimization with Approximate Hessians](https://mlsanity.com/paper/2506.13710/) (2025)
- [Blockwise Stabilized Adaptive Cubic Regularization with Subsolvers via Recurrence](https://mlsanity.com/paper/2608.22129/) (2026)
- [Simple Stepsize for Quasi-Newton Methods with Global Convergence Guarantees](https://mlsanity.com/paper/2508.19712/) (2025)

## Abstract (arXiv)

We propose general non-accelerated and accelerated tensor methods under inexact information on the derivatives of the objective, analyze their convergence rate. Further, we provide conditions for the inexactness in each derivative that is sufficient for each algorithm to achieve the desired accuracy. As a corollary, we propose stochastic tensor methods for convex optimization and obtain sufficient mini-batch sizes for each derivative.