Optimal Accounting of Differential Privacy via Characteristic Function

Yuqing Zhu, Jinshuo Dong, Yu-Xiang Wang
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:4782-4817, 2022.

Abstract

Characterizing the privacy degradation over compositions, i.e., privacy accounting, is a fundamental topic in differential privacy (DP) with many applications to differentially private machine learning and federated learning. We propose a unification of recent advances (Renyi DP, privacy profiles, $f$-DP and the PLD formalism) via the characteristic function ($\phi$-function) of a certain dominating privacy loss random variable. We show that our approach allows natural adaptive composition like Renyi DP, provides exactly tight privacy accounting like PLD, and can be (often losslessly) converted to privacy profile and $f$-DP, thus providing $(\epsilon,\delta)$-DP guarantees and interpretable tradeoff functions. Algorithmically, we propose an analytical Fourier accountant that represents the complex logarithm of $\phi$-functions symbolically and uses Gaussian quadrature for numerical computation. On several popular DP mechanisms and their subsampled counterparts, we demonstrate the flexibility and tightness of our approach in theory and experiments.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-zhu22c, title = { Optimal Accounting of Differential Privacy via Characteristic Function }, author = {Zhu, Yuqing and Dong, Jinshuo and Wang, Yu-Xiang}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {4782--4817}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/zhu22c/zhu22c.pdf}, url = {https://proceedings.mlr.press/v151/zhu22c.html}, abstract = { Characterizing the privacy degradation over compositions, i.e., privacy accounting, is a fundamental topic in differential privacy (DP) with many applications to differentially private machine learning and federated learning. We propose a unification of recent advances (Renyi DP, privacy profiles, $f$-DP and the PLD formalism) via the characteristic function ($\phi$-function) of a certain dominating privacy loss random variable. We show that our approach allows natural adaptive composition like Renyi DP, provides exactly tight privacy accounting like PLD, and can be (often losslessly) converted to privacy profile and $f$-DP, thus providing $(\epsilon,\delta)$-DP guarantees and interpretable tradeoff functions. Algorithmically, we propose an analytical Fourier accountant that represents the complex logarithm of $\phi$-functions symbolically and uses Gaussian quadrature for numerical computation. On several popular DP mechanisms and their subsampled counterparts, we demonstrate the flexibility and tightness of our approach in theory and experiments. } }
Endnote
%0 Conference Paper %T Optimal Accounting of Differential Privacy via Characteristic Function %A Yuqing Zhu %A Jinshuo Dong %A Yu-Xiang Wang %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-zhu22c %I PMLR %P 4782--4817 %U https://proceedings.mlr.press/v151/zhu22c.html %V 151 %X Characterizing the privacy degradation over compositions, i.e., privacy accounting, is a fundamental topic in differential privacy (DP) with many applications to differentially private machine learning and federated learning. We propose a unification of recent advances (Renyi DP, privacy profiles, $f$-DP and the PLD formalism) via the characteristic function ($\phi$-function) of a certain dominating privacy loss random variable. We show that our approach allows natural adaptive composition like Renyi DP, provides exactly tight privacy accounting like PLD, and can be (often losslessly) converted to privacy profile and $f$-DP, thus providing $(\epsilon,\delta)$-DP guarantees and interpretable tradeoff functions. Algorithmically, we propose an analytical Fourier accountant that represents the complex logarithm of $\phi$-functions symbolically and uses Gaussian quadrature for numerical computation. On several popular DP mechanisms and their subsampled counterparts, we demonstrate the flexibility and tightness of our approach in theory and experiments.
APA
Zhu, Y., Dong, J. & Wang, Y.. (2022). Optimal Accounting of Differential Privacy via Characteristic Function . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:4782-4817 Available from https://proceedings.mlr.press/v151/zhu22c.html.

Related Material