High Probability Bounds for Stochastic Subgradient Schemes with Heavy Tailed Noise

TL;DR

This paper develops high probability bounds for stochastic subgradient methods under heavy-tailed noise by using a clipping strategy, achieving near optimal bounds with empirical validation.

Contribution

Introduces a clipping-based approach for stochastic subgradient methods that handles heavy-tailed noise, providing near optimal high probability bounds.

Findings

Clipping strategy effectively manages heavy-tailed noise in subgradient estimates.

Achieves near optimal bounds for classical averaging schemes.

Preliminary experiments support the method's validity.

Abstract

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.