# The Impact of Noise on Evaluation Complexity: The Deterministic Trust-Region Case

arXiv: https://arxiv.org/abs/2104.02519 · HTML: https://mlsanity.com/paper/2104.02519/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Apr 2021.

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

- [Recursive Bound-Constrained AdaGrad with Applications to Multilevel and Domain Decomposition Minimization](https://mlsanity.com/paper/2507.11513/) (2025)
- [Layer-Parallel Training for Transformers](https://mlsanity.com/paper/2601.09026/) (2026)
- [Stochastic Ratios Tracking Algorithm for Large Scale Machine Learning Problems](https://mlsanity.com/paper/2305.09978/) (2023)
- [A Trust-Region Algorithm for Noisy Equality Constrained Optimization](https://mlsanity.com/paper/2411.02665/) (2024)

## Abstract (arXiv)

Intrinsic noise in objective function and derivatives evaluations may cause premature termination of optimization algorithms. Evaluation complexity bounds taking this situation into account are presented in the framework of a deterministic trust-region method. The results show that the presence of intrinsic noise may dominate these bounds, in contrast with what is known for methods in which the inexactness in function and derivatives' evaluations is fully controllable. Moreover, the new analysis provides estimates of the optimality level achievable, should noise cause early termination. It finally sheds some light on the impact of inexact computer arithmetic on evaluation complexity.