  We propose an information-theoretic technique for analyzing privacy
guarantees of online algorithms. Specifically, we demonstrate that differential
privacy guarantees of iterative algorithms can be determined by a direct
application of contraction coefficients derived from strong data processing
inequalities for $f$-divergences. Our technique relies on generalizing the
Dobrushin's contraction coefficient for total variation distance to an
$f$-divergence known as $E_\gamma$-divergence. $E_\gamma$-divergence, in turn,
is equivalent to approximate differential privacy. As an example, we apply our
technique to derive the differential privacy parameters of gradient descent.
Moreover, we also show that this framework can be tailored to batch learning
algorithms that can be implemented with one pass over the training dataset.
