Understanding gradient clipping in private SGD: A geometric perspective

Xiangyi Chen, Steven Wu, Mingyi Hong

Research output: Contribution to journalConference articlepeer-review

Abstract

Deep learning models are increasingly popular in many machine learning applications where the training data may contain sensitive information. To provide formal and rigorous privacy guarantee, many learning systems now incorporate differential privacy by training their models with (differentially) private SGD. A key step in each private SGD update is gradient clipping that shrinks the gradient of an individual example whenever its l2 norm exceeds some threshold. We first demonstrate how gradient clipping can prevent SGD from converging to a stationary point. We then provide a theoretical analysis that fully quantifies the clipping bias on convergence with a disparity measure between the gradient distribution and a geometrically symmetric distribution. Our empirical evaluation further suggests that the gradient distributions along the trajectory of private SGD indeed exhibit symmetric structure that favors convergence. Together, our results provide an explanation why private SGD with gradient clipping remains effective in practice despite its potential clipping bias. Finally, we develop a new perturbation-based technique that can provably correct the clipping bias even for instances with highly asymmetric gradient distributions.

Original languageEnglish (US)
JournalAdvances in Neural Information Processing Systems
Volume2020-December
StatePublished - 2020
Event34th Conference on Neural Information Processing Systems, NeurIPS 2020 - Virtual, Online
Duration: Dec 6 2020Dec 12 2020

Bibliographical note

Funding Information:
The research is supported in part by a NSF grant CMMI-1727757, a Google Faculty Research Award, a J.P. Morgan Faculty Award, and a Facebook Research Award.

Publisher Copyright:
© 2020 Neural information processing systems foundation. All rights reserved.

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