# Trust-Region Methods with Low-Fidelity Objective Models

arXiv: https://arxiv.org/abs/2511.00434 · HTML: https://mlsanity.com/paper/2511.00434/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 13 references that are in the map.
- First posted on arXiv 1 Nov 2025.

## Builds on (most cited first, 5 of 5)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Survey of multifidelity methods in uncertainty propagation, inference, and optimization](https://mlsanity.com/paper/1806.10761/) (2018)
- [Newton Sketch: A Linear-time Optimization Algorithm with Linear-Quadratic Convergence](https://mlsanity.com/paper/1505.02250/) (2015)
- [A stochastic subspace approach to gradient-free optimization in high dimensions](https://mlsanity.com/paper/2003.02684/) (2020)
- [Randomised subspace methods for non-convex optimization, with applications to nonlinear least-squares](https://mlsanity.com/paper/2211.09873/) (2022)

## Abstract (arXiv)

We introduce two multifidelity trust-region methods based on the Magical Trust Region (MTR) framework. MTR augments the classical trust-region step with a secondary, informative direction. In our approaches, the secondary ``magical'' directions are determined by solving coarse trust-region subproblems based on low-fidelity objective models. The first proposed method, Sketched Trust-Region (STR), constructs this secondary direction using a sketched matrix to reduce the dimensionality of the trust-region subproblem. The second method, SVD Trust-Region (SVDTR), defines the magical direction via a truncated singular value decomposition of the dataset, capturing the leading directions of variability. Several numerical examples illustrate the potential gain in efficiency.