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.

本文提出了一种新的加速随机一阶方法 clipped-SSTM，该方法通过剪辑随机梯度结合特殊变体的随机梯度下降法，用于解决具有重尾分布噪声的光滑凸随机优化问题，并推导出了该方法的第一个高概率复杂度界限，证明了其优于同类方法。