Privacy Amplification of Iterative Algorithms via Contraction Coefficients

17 Jan 2020  ·  Shahab Asoodeh, Mario Diaz, Flavio P. Calmon ·

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.

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