Information-Theoretic Generalization Bounds for Stochastic Gradient Descent

• URL: http://arxiv.org/abs/2102.00931v1
• Date: Mon, 1 Feb 2021 16:00:34 GMT
• Title: Information-Theoretic Generalization Bounds for Stochastic Gradient Descent
• Authors: Gergely Neu
• Abstract summary: We provide bounds on the technical error that depend on local statistics. Key factors are the objective variance of the gradients, the smoothness of the gradients, and the sensitivity of the loss function to perturbations. Our key tool is combining the information-theoretic generalization bounds previously used for analyzing randomized variants of SGD with perturbation analysis of the paths.
• Score: 13.757095663704858
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the generalization properties of the popular stochastic gradient descent method for optimizing general non-convex loss functions. Our main contribution is providing upper bounds on the generalization error that depend on local statistics of the stochastic gradients evaluated along the path of iterates calculated by SGD. The key factors our bounds depend on are the variance of the gradients (with respect to the data distribution) and the local smoothness of the objective function along the SGD path, and the sensitivity of the loss function to perturbations to the final output. Our key technical tool is combining the information-theoretic generalization bounds previously used for analyzing randomized variants of SGD with a perturbation analysis of the iterates.

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