We investigate the framework of privacy amplification by iteration, recently proposed by Feldman et al., from an information-theoretic lens. We demonstrate that differential privacy guarantees of iterative mappings can be determined by a direct application of contraction coefficients derived from strong data processing inequalities for $f$-divergences. In particular, by generalizing the Dobrushin's contraction coefficient for total variation distance to an $f$-divergence known as $E_{\gamma}$-divergence, we derive tighter bounds on the differential privacy parameters of the projected noisy stochastic gradient descent algorithm with hidden intermediate updates.

中文翻译：

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通过收缩系数对迭代算法进行隐私放大

我们从信息理论的角度研究了最近由 Feldman 等人提出的迭代隐私放大框架。我们证明了迭代映射的差分隐私保证可以通过直接应用从强数据处理不等式导出的收缩系数来确定。特别是，通过将总变异距离的 Dobrushin 收缩系数推广到称为 $E_{\gamma}$-divergence 的 $f$-divergence，我们推导出更严格的投影噪声随机梯度下降算法的差分隐私参数的界限隐藏的中间更新。