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Faster Privacy Accounting via Evolving Discretization
Badih Ghazi · Pritish Kamath · Ravi Kumar · Pasin Manurangsi

Wed Jul 20 03:30 PM -- 05:30 PM (PDT) @ Hall E #1019
We introduce a new algorithm for numerical composition of privacy random variables, useful for computing the accurate differential privacy parameters for compositions of mechanisms.Our algorithm achieves a running time and memory usage of $\polylog(k)$ for the task of self-composing a broad class of mechanisms $k$ times; this class, e.g., includes the sub-sampled Gaussian mechanism, that appears in the analysis of differentially private stochastic gradient descent (DP-SGD).By comparison, recent work by Gopi et al. (NeurIPS 2021) has obtained a running time of $\wtilde{O}(\sqrt{k})$ for the same task.Our approach extends to the case of composing $k$ different mechanisms in the same class, improving upon the running time and memory usage in their work from $\wtilde{O}(k^{1.5})$ to $\wtilde{O}(k)$.

Author Information

Badih Ghazi (Google)
Pritish Kamath (Google Research)
Ravi Kumar (Google)
Pasin Manurangsi (Google Research)

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