We consider the problem of empirical risk minimization given a database, using the gradient descent algorithm. We note that the function to be optimized may be non-convex, consisting of saddle points which impede the convergence of the algorithm. A perturbed gradient descent algorithm is typically employed to escape these saddle points. We show that this algorithm, that perturbs the gradient, inherently preserves the privacy of the data. We then employ the differential privacy framework to quantify the privacy hence achieved. We also analyze the change in privacy with varying parameters such as problem dimension and the distance between the databases.

中文翻译：

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扰动梯度下降的差分私有性质

我们考虑使用梯度下降算法在给定数据库的情况下将经验风险最小化的问题。我们注意到，要优化的函数可能是非凸的，由阻碍算法收敛的鞍点组成。通常采用扰动梯度下降算法来逃避这些鞍点。我们证明了这种扰动梯度的算法固有地保留了数据的私密性。然后，我们采用差分隐私框架来量化由此获得的隐私。我们还使用各种参数（例如问题维度和数据库之间的距离）来分析隐私的变化。