Differentially Private Accelerated Optimization Algorithms

We present two classes of differentially private optimization algorithms derived from the well-known accelerated first-order methods. The first algorithm is inspired by Polyak's heavy ball method and employs a smoothing approach to decrease the accumulated noise on the gradient steps required f...

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Bibliographic Details
Published in:arXiv.org 2020-08
Main Authors: Kuru, Nurdan, \c{S} İlker Birbil, Gurbuzbalaban, Mert, Yildirim, Sinan
Format: Article
Language:English
Subjects:
Algorithms
Optimization
Optimization algorithms
Privacy
Systems analysis
Online Access:Get full text
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Summary:We present two classes of differentially private optimization algorithms derived from the well-known accelerated first-order methods. The first algorithm is inspired by Polyak's heavy ball method and employs a smoothing approach to decrease the accumulated noise on the gradient steps required for differential privacy. The second class of algorithms are based on Nesterov's accelerated gradient method and its recent multi-stage variant. We propose a noise dividing mechanism for the iterations of Nesterov's method in order to improve the error behavior of the algorithm. The convergence rate analyses are provided for both the heavy ball and the Nesterov's accelerated gradient method with the help of the dynamical system analysis techniques. Finally, we conclude with our numerical experiments showing that the presented algorithms have advantages over the well-known differentially private algorithms.
ISSN:2331-8422
DOI:10.48550/arxiv.2008.01989