Stochastic Optimization with Heavy-Tailed Noise via Accelerated Gradient Clipping

• URL: http://arxiv.org/abs/2005.10785v2
• Date: Fri, 23 Oct 2020 11:00:08 GMT
• Title: Stochastic Optimization with Heavy-Tailed Noise via Accelerated Gradient Clipping
• Authors: Eduard Gorbunov, Marina Danilova, Alexander Gasnikov
• Abstract summary: We propose a new accelerated first-order method called clipped-SSTM for smooth convex optimization with heavy-tailed distributed noise in gradients. We prove new complexity that outperform state-of-the-art results in this case. We derive the first non-trivial high-probability complexity bounds for SGD with clipping without light-tails assumption on the noise.
• Score: 69.9674326582747
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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