# Stochastic Trust Region Methods with Trust Region Radius Depending on Probabilistic Models

arXiv: https://arxiv.org/abs/1904.03342 · HTML: https://mlsanity.com/paper/1904.03342/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Apr 2019.

## Built on by (most cited first, 4 of 4)

- [Riemannian Natural Gradient Methods](https://mlsanity.com/paper/2207.07287/) (2022)
- [Two trust region type algorithms for solving nonconvex-strongly concave minimax problems](https://mlsanity.com/paper/2402.09807/) (2024)
- [On the efficiency of Stochastic Quasi-Newton Methods for Deep Learning](https://mlsanity.com/paper/2205.09121/) (2022)
- [Stochastic Trust-Region Methods for Over-parameterized Models](https://mlsanity.com/paper/2604.14017/) (2026)

## Abstract (arXiv)

We present a stochastic trust-region model-based framework in which its radius is related to the probabilistic models. Especially, we propose a specific algorithm, termed STRME, in which the trust-region radius depends linearly on the latest model gradient. The complexity of STRME method in non-convex, convex and strongly convex settings has all been analyzed, which matches the existing algorithms based on probabilistic properties. In addition, several numerical experiments are carried out to reveal the benefits of the proposed methods compared to the existing stochastic trust-region methods and other relevant stochastic gradient methods.