# Sequential convergence of AdaGrad algorithm for smooth convex optimization

arXiv: https://arxiv.org/abs/2011.12341 · HTML: https://mlsanity.com/paper/2011.12341/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Nov 2020.

## Built on by (most cited first, 5 of 5)

- [DoWG Unleashed: An Efficient Universal Parameter-Free Gradient Descent Method](https://mlsanity.com/paper/2305.16284/) (2023)
- [Automated Few-Shot Time Series Forecasting based on Bi-level Programming](https://mlsanity.com/paper/2203.03328/) (2022)
- [Randomized Feasibility Methods for Constrained Optimization with Adaptive Step Sizes](https://mlsanity.com/paper/2601.20076/) (2026)
- [AdaGrad-Diff: A New Version of the Adaptive Gradient Algorithm](https://mlsanity.com/paper/2602.13112/) (2026)
- [A regret minimization approach to fixed-point iterations](https://mlsanity.com/paper/2509.21653/) (2025)

## Abstract (arXiv)

We prove that the iterates produced by, either the scalar step size variant, or the coordinatewise variant of AdaGrad algorithm, are convergent sequences when applied to convex objective functions with Lipschitz gradient. The key insight is to remark that such AdaGrad sequences satisfy a variable metric quasi-Fej'er monotonicity property, which allows to prove convergence.