# A non-monotone trust-region method with noisy oracles and additional sampling

arXiv: https://arxiv.org/abs/2307.10038 · HTML: https://mlsanity.com/paper/2307.10038/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jul 2023.

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

- [A Trust-Region Algorithm for Noisy Equality Constrained Optimization](https://mlsanity.com/paper/2411.02665/) (2024)

## Abstract (arXiv)

In this work, we introduce a novel stochastic second-order method, within the framework of a non-monotone trust-region approach, for solving the unconstrained, nonlinear, and non-convex optimization problems arising in the training of deep neural networks. The proposed algorithm makes use of subsampling strategies which yield noisy approximations of the finite sum objective function and its gradient. To effectively control the resulting approximation error, we introduce an adaptive sample size strategy based on inexpensive additional sampling. Depending on the estimated progress of the algorithm, this can yield sample size scenarios ranging from mini-batch to full sample functions. We provide convergence analysis for all possible scenarios and show that the proposed method achieves almost sure convergence under standard assumptions for the trust-region framework. We report numerical experiments showing that the proposed algorithm outperforms its state-of-the-art counterpart in deep neural network training for image classification and regression tasks while requiring a significantly smaller number of gradient evaluations.