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In this work we study high probability bounds for stochastic subgradientmethods under heavy tailed noise. In this case the noise is only assumed tohave finite variance as opposed to a sub-Gaussian distribution for which it isknown that standard subgradient methods enjoys high probability bounds. Weanalyzed a clipped version of the projected stochastic subgradient method,where subgradient estimates are truncated whenever they have large norms. Weshow that this clipping strategy leads both to near optimal any-time and finitehorizon bounds for many classical averaging schemes. Preliminary experimentsare shown to support the validity of the method.

High Probability Bounds for Stochastic Subgradient Schemes with Heavy Tailed Noise