Optimal Accounting of Differential Privacy via Characteristic Function

• URL: http://arxiv.org/abs/2106.08567v1
• Date: Wed, 16 Jun 2021 06:13:23 GMT
• Title: Optimal Accounting of Differential Privacy via Characteristic Function
• Authors: Yuqing Zhu, Jinshuo Dong and Yu-Xiang Wang
• Abstract summary: 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 worst-case'' 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.
• Score: 25.78065563380023
• License: http://creativecommons.org/licenses/by/4.0/
• 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 ``worst-case'' 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.

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