  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.
