In this work we study high probability bounds for stochastic subgradient methods under heavy tailed noise. In this setting the noise is only assumed to have finite variance as opposed to a sub-Gaussian distribution for which it is known that standard subgradient methods enjoys high probability bounds. We analyzed a clipped version of the projected stochastic subgradient method, where subgradient estimates are truncated whenever they have large norms. We show that this clipping strategy leads both to near optimal any-time and finite horizon bounds for many classical averaging schemes. Preliminary experiments are shown to support the validity of the method.
@article{arxiv.2208.08567,
title = {High Probability Bounds for Stochastic Subgradient Schemes with Heavy Tailed Noise},
author = {Daniela A. Parletta and Andrea Paudice and Massimiliano Pontil and Saverio Salzo},
journal= {arXiv preprint arXiv:2208.08567},
year = {2024}
}