# An Improved Analysis of the Clipped Stochastic subGradient Method under Heavy-Tailed Noise

arXiv: https://arxiv.org/abs/2410.00573 · HTML: https://mlsanity.com/paper/2410.00573/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Oct 2024.

## Built on by (most cited first, 3 of 3)

- [Online Convex Optimization with Heavy Tails: Old Algorithms, New Regrets, and Applications](https://mlsanity.com/paper/2508.07473/) (2025)
- [In-Expectation Convergence of Stochastic Gradient Methods under Heavy-Tailed Noise](https://mlsanity.com/paper/2606.00520/) (2026)
- [New Bounds for the Last Iterate of the Stochastic subGradient Method](https://mlsanity.com/paper/2606.24879/) (2026)

## Abstract (arXiv)

In this paper, we provide novel optimal (or near optimal) convergence rates for a clipped version of the stochastic subgradient method. We consider nonsmooth convex problems over possibly unbounded domains, under heavy-tailed noise that possesses only the first p moments for p ∈ left]1,2right]. For the last iterate, we establish convergence in expectation for the objective values with rates of order (log1/p k)/k(p-1)/p and 1/k(p-1)/p, for anytime and finite-horizon respectively. We also derive new convergence rates, in expectation and with high probability, for the objective values along the average iterates--improving existing results by a log(2p-1)/p k factor. Those results are applied to the problem of supervised learning with kernels demonstrating the effectiveness of our theory. Finally, we give preliminary experiments.