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北美退伍军人节(Veterans Day),12 日无更新
arXiv 2008.01989cs.LGcs.CRmath.OCstat.ML
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差分私有加速优化算法

Differentially Private Accelerated Optimization Algorithms

Sabancı University(萨班哲大学);Erasmus University(伊拉斯姆斯大学);Rutgers University(罗格斯大学)

Nurdan Kuru, Ş. İlker Birbil, Mert Gurbuzbalaban, Sinan Yildirim

摘要:

我们提出了两类差分私有优化算法的著名的加速一阶方法。第一种算法受Polyak的重球方法的启发,采用平滑方法来减少差分隐私所需的梯度步长上的累积噪声。第二类算法是基于Nesterov的加速梯度法及其最近的多阶段变体。我们提出了一个噪声划分机制的Nesterov的方法的迭代,以改善算法的错误行为。借助动力系统分析技术,对重球法和Nesterov加速梯度法进行了收敛速度分析。最后,我们得出结论,我们的数值实验表明,所提出的算法具有优势,比著名的差分隐私算法。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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