标题： Renyi差分隐私的非平滑正则化优化的ADMM方法 显示英文标题

标题： Renyi Differentially Private ADMM for Non-Smooth Regularized Optimization

摘要： 本文研究了在Rényi微分隐私（RDP）下最小化由可微凸损失函数与非光滑正则项（如$L_1$范数或核范数）组成的复合目标函数的问题。 为了解决该问题，我们提出了两种随机交替方向乘子法（ADMM）算法：基于梯度扰动的ssADMM和基于输出扰动的mpADMM。 这两种算法都将原始问题分解为具有闭式解的子问题。 第一个算法ssADMM利用RDP的最新隐私放大结果来减少需要添加的噪声量。 第二个算法mpADMM数值计算了ADMM变量更新的敏感性，并在每个周期结束时发布更新后的参数向量。 我们在真实数据集和模拟数据集上将我们的算法性能与几种基准算法进行了比较。 实验结果表明，在高隐私设置（小$\epsilon$）下，ssADMM和mpADMM分别在分类和特征选择性能方面优于其他基准算法。 显示英文摘要

摘要： In this paper we consider the problem of minimizing composite objective functions consisting of a convex differentiable loss function plus a non-smooth regularization term, such as $L_1$ norm or nuclear norm, under R\'enyi differential privacy (RDP). To solve the problem, we propose two stochastic alternating direction method of multipliers (ADMM) algorithms: ssADMM based on gradient perturbation and mpADMM based on output perturbation. Both algorithms decompose the original problem into sub-problems that have closed-form solutions. The first algorithm, ssADMM, applies the recent privacy amplification result for RDP to reduce the amount of noise to add. The second algorithm, mpADMM, numerically computes the sensitivity of ADMM variable updates and releases the updated parameter vector at the end of each epoch. We compare the performance of our algorithms with several baseline algorithms on both real and simulated datasets. Experimental results show that, in high privacy regimes (small $\epsilon$), ssADMM and mpADMM outperform other baseline algorithms in terms of classification and feature selection performance, respectively.