Noisy Truncated SGD: Optimization and Generalization

• URL: http://arxiv.org/abs/2103.00075v1
• Date: Fri, 26 Feb 2021 22:39:41 GMT
• Title: Noisy Truncated SGD: Optimization and Generalization
• Authors: Yingxue Zhou, Xinyan Li, Arindam Banerjee
• Abstract summary: Recent empirical work on SGD has shown that most gradient components over epochs are quite small. Inspired by such a study, we rigorously study properties of noisy SGD (NT-SGD) We prove that NT-SGD can provably escape from saddle points and requires less noise compared to previous related work.
• Score: 27.33458360279836
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recent empirical work on SGD applied to over-parameterized deep learning has shown that most gradient components over epochs are quite small. Inspired by such observations, we rigorously study properties of noisy truncated SGD (NT-SGD), a noisy gradient descent algorithm that truncates (hard thresholds) the majority of small gradient components to zeros and then adds Gaussian noise to all components. Considering non-convex smooth problems, we first establish the rate of convergence of NT-SGD in terms of empirical gradient norms, and show the rate to be of the same order as the vanilla SGD. Further, we prove that NT-SGD can provably escape from saddle points and requires less noise compared to previous related work. We also establish a generalization bound for NT-SGD using uniform stability based on discretized generalized Langevin dynamics. Our experiments on MNIST (VGG-5) and CIFAR-10 (ResNet-18) demonstrate that NT-SGD matches the speed and accuracy of vanilla SGD, and can successfully escape sharp minima while having better theoretical properties.

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