# Matrix-Free Preconditioning in Online Learning

arXiv: https://arxiv.org/abs/1905.12721 · HTML: https://mlsanity.com/paper/1905.12721/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2019.

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

- [Parameter-free Mirror Descent](https://mlsanity.com/paper/2203.00444/) (2022)
- [Fully Unconstrained Online Learning](https://mlsanity.com/paper/2405.20540/) (2024)
- [Implicit Parameter-free Online Learning with Truncated Linear Models](https://mlsanity.com/paper/2203.10327/) (2022)
- [On the Initialization for Convex-Concave Min-max Problems](https://mlsanity.com/paper/2103.00284/) (2021)
- [Eventually LIL Regret: Almost Sure lnln T Regret for a sub-Gaussian Mixture on Unbounded Data](https://mlsanity.com/paper/2512.12325/) (2025)

## Abstract (arXiv)

We provide an online convex optimization algorithm with regret that interpolates between the regret of an algorithm using an optimal preconditioning matrix and one using a diagonal preconditioning matrix. Our regret bound is never worse than that obtained by diagonal preconditioning, and in certain setting even surpasses that of algorithms with full-matrix preconditioning. Importantly, our algorithm runs in the same time and space complexity as online gradient descent. Along the way we incorporate new techniques that mildly streamline and improve logarithmic factors in prior regret analyses. We conclude by benchmarking our algorithm on synthetic data and deep learning tasks.