# An Additively Preconditioned Trust Region Strategy for Machine Learning

arXiv: https://arxiv.org/abs/2512.14286 · HTML: https://mlsanity.com/paper/2512.14286/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Dec 2025.

## Built on by (most cited first, 1 of 1)

- [A Non-Monotone Preconditioned Trust-Region Method for Neural Network Training](https://mlsanity.com/paper/2605.14860/) (2026)

## Abstract (arXiv)

Modern machine learning, especially the training of deep neural networks, depends on solving large-scale, highly nonconvex optimization problems, whose objective function exhibit a rough landscape. Motivated by the success of parallel preconditioners in the context of Krylov methods for large scale linear systems, we introduce a novel nonlinearly preconditioned Trust-Region method that makes use of an additive Schwarz correction at each minimization step, thereby accelerating convergence. More precisely, we propose a variant of the Additively Preconditioned Trust-Region Strategy (APTS), which combines a right-preconditioned additive Schwarz framework with a classical Trust-Region algorithm. By decomposing the parameter space into sub-domains, APTS solves local non-linear sub-problems in parallel and assembles their corrections additively. The resulting method not only shows fast convergence; due to the underlying Trust-Region strategy, it furthermore largely obviates the need for hyperparameter tuning.