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arXiv · 2207.04381

Faster Privacy Accounting via Evolving Discretization

Badih Ghazi·Pritish Kamath·Ravi Kumar·Pasin Manurangsi
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Abstract

We introduce a new algorithm for numerical composition of privacy random variables, useful for computing the accurate differential privacy parameters for composition of mechanisms. Our algorithm achieves a running time and memory usage of $\mathrm{polylog}(k)$ for the task of self-composing a mechanism, from 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. By comparison, recent work by Gopi et al. (NeurIPS 2021) has obtained a running time of $\widetilde{O}(\sqrt{k})$ for the same task. Our approach extends to the case of composing $k$ different mechanisms in the same class, improving upon their running time and memory usage from $\widetilde{O}(k^{1.5})$ to $\widetilde{O}(k)$.

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Badih Ghazi, Pritish Kamath, Ravi Kumar, Pasin Manurangsi. 2022-07-10. Faster Privacy Accounting via Evolving Discretization. https://arxiv.org/abs/2207.04381

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