Privacy Amplification of Iterative Algorithms via Contraction Coefficients

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