# On Robustness of the Normalized Subgradient Method with Randomly Corrupted Subgradients

arXiv: https://arxiv.org/abs/2009.13725 · HTML: https://mlsanity.com/paper/2009.13725/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Sep 2020.

## Built on by (most cited first, 1 of 1)

- [Robust Distributed Optimization With Randomly Corrupted Gradients](https://mlsanity.com/paper/2106.14956/) (2021)

## Abstract (arXiv)

Numerous modern optimization and machine learning algorithms rely on subgradient information being trustworthy and hence, they may fail to converge when such information is corrupted. In this paper, we consider the setting where subgradient information may be arbitrarily corrupted (with a given probability) and study the robustness properties of the normalized subgradient method. Under the probabilistic corruption scenario, we prove that the normalized subgradient method, whose updates rely solely on directional information of the subgradient, converges to a minimizer for convex, strongly convex, and weakly-pseudo convex functions satisfying certain conditions. Numerical evidence on linear regression and logistic classification problems support our results.