扰动目标上梯度下降的差分隐私研究

1. 12:00
   arXiv · Statistics Machine Learning

   目标扰动下梯度下降的差分隐私

   论文研究在正则化经验风险上加入随机线性项后，释放确定性梯度下降第 N 次迭代而非精确极小点的差分隐私。在目标函数强凸光滑且 Hessian 满足 Lipschitz 条件下，证明 z 到 w_N 的映射为 C¹ 微分同胚，隐私界不含显式环境维度因子，迭代修正项几何递减。期望超额经验风险上界为 dσ²/(2μ) 加几何递减优化项，并可转移到总体风险。

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