# Domain-independent Dominance of Adaptive Methods

arXiv: https://arxiv.org/abs/1912.01823 · HTML: https://mlsanity.com/paper/1912.01823/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Dec 2019.

## Built on by (most cited first, 13 of 13)

- [The Power of Adaptivity in SGD: Self-Tuning Step Sizes with Unbounded Gradients and Affine Variance](https://mlsanity.com/paper/2202.05791/) (2022)
- [Permutation Search of Tensor Network Structures via Local Sampling](https://mlsanity.com/paper/2206.06597/) (2022)
- [Convergence Rate Analysis of LION](https://mlsanity.com/paper/2411.07724/) (2024)
- [Accelerated Training via Incrementally Growing Neural Networks using Variance Transfer and Learning Rate Adaptation](https://mlsanity.com/paper/2306.12700/) (2023)
- [On the O(frac√dK1/4) Convergence Rate of AdamW Measured by ℓ1 Norm](https://mlsanity.com/paper/2505.11840/) (2025)
- [Rethinking Adam: A Twofold Exponential Moving Average Approach](https://mlsanity.com/paper/2106.11514/) (2021)
- [Momentum Centering and Asynchronous Update for Adaptive Gradient Methods](https://mlsanity.com/paper/2110.05454/) (2021)
- [Formal guarantees for heuristic optimization algorithms used in machine learning](https://mlsanity.com/paper/2208.00502/) (2022)
- [Fine-Tuning Adaptive Stochastic Optimizers: Determining the Optimal Hyperparameter ε via Gradient Magnitude Histogram Analysis](https://mlsanity.com/paper/2311.11532/) (2023)
- [On the O(frac√dT1/4) Convergence Rate of RMSProp and Its Momentum Extension Measured by ℓ1 Norm](https://mlsanity.com/paper/2402.00389/) (2024)
- [Anon: Extrapolating Adaptivity Beyond SGD and Adam](https://mlsanity.com/paper/2605.02317/) (2026)
- [Why Clipping Matters in AdaGrad? Toward a High-Probability Theory under Generalized Smoothness](https://mlsanity.com/paper/2609.30276/) (2026)
- [Minimax Optimality of Shampoo for Nonstationary Stochastic Optimization](https://mlsanity.com/paper/2610.16923/) (2026)

## Abstract (arXiv)

From a simplified analysis of adaptive methods, we derive AvaGrad, a new optimizer which outperforms SGD on vision tasks when its adaptability is properly tuned. We observe that the power of our method is partially explained by a decoupling of learning rate and adaptability, greatly simplifying hyperparameter search. In light of this observation, we demonstrate that, against conventional wisdom, Adam can also outperform SGD on vision tasks, as long as the coupling between its learning rate and adaptability is taken into account. In practice, AvaGrad matches the best results, as measured by generalization accuracy, delivered by any existing optimizer (SGD or adaptive) across image classification (CIFAR, ImageNet) and character-level language modelling (Penn Treebank) tasks.