# Asymptotic Analysis of Conditioned Stochastic Gradient Descent

arXiv: https://arxiv.org/abs/2006.02745 · HTML: https://mlsanity.com/paper/2006.02745/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jun 2020.

## Built on by (most cited first, 4 of 4)

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- [Online Statistical Inference of Constrained Stochastic Optimization via Random Scaling](https://mlsanity.com/paper/2505.18327/) (2025)
- [TR-SSQP: A Trust-Region Method for Constrained Stochastic Optimization under Heavy-Tailed Noise](https://mlsanity.com/paper/2609.30732/) (2026)

## Abstract (arXiv)

In this paper, we investigate a general class of stochastic gradient descent (SGD) algorithms, called Conditioned SGD, based on a preconditioning of the gradient direction. Using a discrete-time approach with martingale tools, we establish under mild assumptions the weak convergence of the rescaled sequence of iterates for a broad class of conditioning matrices including stochastic first-order and second-order methods. Almost sure convergence results, which may be of independent interest, are also presented. Interestingly, the asymptotic normality result consists in a stochastic equicontinuity property so when the conditioning matrix is an estimate of the inverse Hessian, the algorithm is asymptotically optimal.