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Numerical Composition of Differential Privacy
Sivakanth Gopi · Yin Tat Lee · Lukas Wutschitz

Thu Dec 09 12:30 AM -- 02:00 AM (PST) @
We give a fast algorithm to compose privacy guarantees of differentially private (DP) algorithms to arbitrary accuracy. Our method is based on the notion of privacy loss random variables to quantify the privacy loss of DP algorithms. The running time and memory needed for our algorithm to approximate the privacy curve of a DP algorithm composed with itself $k$ times is $\tilde{O}(\sqrt{k})$. This improves over the best prior method by Koskela et al. (2020) which requires $\tilde{\Omega}(k^{1.5})$ running time. We demonstrate the utility of our algorithm by accurately computing the privacy loss of DP-SGD algorithm of Abadi et al. (2016) and showing that our algorithm speeds up the privacy computations by a few orders of magnitude compared to prior work, while maintaining similar accuracy.

Author Information

Sivakanth Gopi (Microsoft Research)

Sivakanth Gopi is a senior researcher in the Algorithms group at Microsoft Research Redmond. He is interested in Coding Theory and Differential Privacy.

Yin Tat Lee (UW)
Lukas Wutschitz (Microsoft)

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