Stochastic Optimization with Heavy-Tailed Noise via Accelerated Gradient Clipping

Part of Advances in Neural Information Processing Systems 33 pre-proceedings (NeurIPS 2020)

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Eduard Gorbunov, Marina Danilova, Alexander Gasnikov


<p>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. </p>