# AdaGrad does not adapt to H"older-smoothness for composite objectives

arXiv: https://arxiv.org/abs/2606.29893 · HTML: https://mlsanity.com/paper/2606.29893/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 7 references that are in the map.
- First posted on arXiv 29 Jun 2026.

## Builds on (most cited first, 4 of 4)

- [Online Adaptive Methods, Universality and Acceleration](https://mlsanity.com/paper/1809.02864/) (2018)
- [Normalized Gradients for All](https://mlsanity.com/paper/2308.05621/) (2023)
- [AdaGrad-Diff: A New Version of the Adaptive Gradient Algorithm](https://mlsanity.com/paper/2602.13112/) (2026)
- [Universal Adaptive Proximal Gradient Methods via Gradient Mapping Accumulation](https://mlsanity.com/paper/2605.05944/) (2026)

## Abstract (arXiv)

We exhibit a simple deterministic one-dimensional convex composite optimization problem for which AdaGrad scheme does not achieve the classical convergence rate O(n-(1+nu)/2) associated with H"older-smooth objectives. The example highlights a basic mismatch between classical AdaGrad accumulation and composite optimality. A main insight is that the gradient of the smooth term may not vanish at the optimum, causing AdaGrad to keep reducing its stepsize excessively and converge more slowly. We also discuss why alternative accumulation mechanisms based on gradient mappings or on successive gradient differences, avoid this pathology.