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 accumulated noise on gradient steps required for differential privacy. second class are based Nesterov's its recent multistage variant. propose dividing mechanism iterations in order improve error behavior algorithm. convergence rate analyses provided both with help dynamical system analysis techniques. Finally, we conclude our numerical experiments showing that presented have advantages over algorithms.