Differentially Private Accelerated Optimization Algorithms
This work addresses the need for more efficient privacy-preserving optimization in machine learning, representing an incremental improvement over prior methods.
The paper tackles the problem of optimizing differentially private algorithms by introducing two classes derived from accelerated first-order methods, resulting in improved error behavior and advantages over existing differentially private algorithms as shown in numerical experiments.
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.