Differentially Private Accelerated Optimization Algorithms

TL;DR

This paper introduces two novel differentially private accelerated optimization algorithms based on classical methods, improving privacy-utility trade-offs through smoothing and noise dividing techniques, with theoretical convergence guarantees and empirical validation.

Contribution

It develops two new differentially private accelerated algorithms inspired by Polyak's and Nesterov's methods, incorporating smoothing and noise dividing strategies for better performance.

Findings

Algorithms achieve improved privacy-utility balance.

Convergence rates are established via dynamical system analysis.

Numerical experiments demonstrate advantages over existing methods.

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 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.