Faster Privacy Accounting via Evolving Discretization
Badih Ghazi, Pritish Kamath, Ravi Kumar, Pasin Manurangsi
Abstract
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 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 (DP-SGD). 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 the running time and memory usage in their work from $\widetilde{O}(k^{1.5})$ to $\wtilde{O}(k)$.
BibTeX
@InProceedings{pmlr-v162-ghazi22a,
title = {Faster Privacy Accounting via Evolving Discretization},
author = {Ghazi, Badih and Kamath, Pritish and Kumar, Ravi and Manurangsi, Pasin},
booktitle = {Proceedings of the 39th International Conference on Machine Learning},
pages = {7470--7483},
year = {2022},
editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan},
volume = {162},
series = {Proceedings of Machine Learning Research},
month = {17--23 Jul},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v162/ghazi22a/ghazi22a.pdf},
url = {https://proceedings.mlr.press/v162/ghazi22a.html},
abstract = {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 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 (DP-SGD). 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 the running time and memory usage in their work from $\widetilde{O}(k^{1.5})$ to $\wtilde{O}(k)$.}
}