# Gradient-only line searches: An Alternative to Probabilistic Line Searches

arXiv: https://arxiv.org/abs/1903.09383 · HTML: https://mlsanity.com/paper/1903.09383/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Mar 2019.

## Built on by (most cited first, 3 of 3)

- [GOALS: Gradient-Only Approximations for Line Searches Towards Robust and Consistent Training of Deep Neural Networks](https://mlsanity.com/paper/2105.10915/) (2021)
- [Using a one dimensional parabolic model of the full-batch loss to estimate learning rates during training](https://mlsanity.com/paper/2108.13880/) (2021)
- [Maximum Tsallis Entropy Distributions for Robust and Efficient Sparse Learning from Correlated Data](https://mlsanity.com/paper/2608.17244/) (2026)

## Abstract (arXiv)

Step sizes in neural network training are largely determined using predetermined rules such as fixed learning rates and learning rate schedules. These require user input or expensive global optimization strategies to determine their functional form and associated hyperparameters. Line searches are capable of adaptively resolving learning rate schedules. However, due to discontinuities induced by mini-batch sub-sampling, they have largely fallen out of favour. Notwithstanding, probabilistic line searches, which use statistical surrogates over a limited spatial domain, have recently demonstrated viability in resolving learning rates for stochastic loss functions. This paper introduces an alternative paradigm, Gradient-Only Line Searches that are Inexact (GOLS-I), as an alternative strategy to automatically determine learning rates in stochastic loss functions over a range of 15 orders of magnitude without the use of surrogates. We show that GOLS-I is a competitive strategy to reliably determine step sizes, adding high value in terms of performance, while being easy to implement.