Differentially private accelerated optimization algorithms

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Kuru, Nurdan and Birbil, Ş. İlker and Gürbüzbalaban, Mert and Yıldırım, Sinan (2022) Differentially private accelerated optimization algorithms. SIAM Journal on Optimization, 32 (2). pp. 795-821. ISSN 1052-6234 (Print) 1095-7189 (Online)

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Abstract

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 multistage 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.
Item Type: Article
Uncontrolled Keywords: differential privacy, accelerated optimization methods
Subjects: Q Science > QA Mathematics > QA273-280 Probabilities. Mathematical statistics
T Technology > T Technology (General) > T055.4-60.8 Industrial engineering. Management engineering
T Technology > T Technology (General) > T055.4-60.8 Industrial engineering. Management engineering > T57.6-57.97 Operations research. Systems analysis
Divisions: Faculty of Engineering and Natural Sciences > Academic programs > Computer Science & Eng.
Faculty of Engineering and Natural Sciences > Academic programs > Industrial Engineering
Faculty of Engineering and Natural Sciences
Depositing User: Sinan Yıldırım
Date Deposited: 23 Jun 2022 15:21
Last Modified: 23 Aug 2022 15:08
URI: https://research.sabanciuniv.edu/id/eprint/42844

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