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

## TL;DR

This paper introduces a stochastic trust-region method called STRME, where the trust-region radius depends on probabilistic models and the latest gradient, with analyzed complexity and demonstrated benefits through numerical experiments.

## Contribution

The paper proposes a novel stochastic trust-region algorithm with a radius linearly dependent on the latest gradient, and provides complexity analysis and empirical validation.

## Key findings

- STRME matches existing algorithms in complexity analysis.
- Numerical experiments show STRME outperforms existing stochastic trust-region methods.
- The trust-region radius dependence improves convergence behavior.

## Abstract

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.