Privacy Amplification of Iterative Algorithms via Contraction Coefficients

01/17/2020

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by   Shahab Asoodeh, et al.

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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_γ-divergence, we derive tighter bounds on the differential privacy parameters of the projected noisy stochastic gradient descent algorithm with hidden intermediate updates.