In this paper, we propose a new accelerated stochastic first-order method called clipped-SSTM for smooth convex stochastic optimization with heavy-tailed distributed noise in stochastic gradients and derive the first high-probability complexity bounds for this method closing the gap in the theory of stochastic optimization with heavy-tailed noise. Our method is based on a special variant of accelerated Stochastic Gradient Descent (SGD) and clipping of stochastic gradients. We extend our method to the strongly convex case and prove new complexity bounds that outperform state-of-the-art results in this case. Finally, we extend our proof technique and derive the first non-trivial high-probability complexity bounds for SGD with clipping without light-tails assumption on the noise.
@article{arxiv.2005.10785,
title = {Stochastic Optimization with Heavy-Tailed Noise via Accelerated Gradient Clipping},
author = {Eduard Gorbunov and Marina Danilova and Alexander Gasnikov},
journal= {arXiv preprint arXiv:2005.10785},
year = {2020}
}