# Unified Enhancement of Privacy Bounds for Mixture Mechanisms via $f$-Differential Privacy

Source: [Unified Enhancement of Privacy Bounds for Mixture Mechanisms via $f$-Differential Privacy](<https://www.sota2.com/research/paper/68fa5b0a1e209131ce9c4bb1>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-12-24T11:45:19.545Z

Authors: Chendi Wang, Buxin Su, Jiayuan Ye, Reza Shokri, Weijie J. Su

Published: 2023-10-30T19:37:51.000Z

## Abstract

Differentially private (DP) machine learning algorithms incur many sources of randomness, such as random initialization, random batch subsampling, and shuffling. However, such randomness is difficult to take into account when proving differential privacy bounds because it induces mixture distributions for the algorithm's output that are difficult to analyze. This paper focuses on improving privacy bounds for shuffling models and one-iteration differentially private gradient descent (DP-GD) with random initializations using $f$-DP. We derive a closed-form expression of the trade-off function for shuffling models that outperforms the most up-to-date results based on $(\\epsilon,\\delta)$-DP. Moreover, we investigate the effects of random initialization on the privacy of one-iteration DP-GD. Our numerical computations of the trade-off function indicate that random initialization can enhance the privacy of DP-GD. Our analysis of $f$-DP guarantees for these mixture mechanisms relies on an inequality for trade-off functions introduced in this paper. This inequality implies the joint convexity of $F$-divergences. Finally, we study an $f$-DP analog of the advanced joint convexity of the hockey-stick divergence related to $(\\epsilon,\\delta)$-DP and apply it to analyze the privacy of mixture mechanisms.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Privacy Budget Estimation on Shuffled Mechanisms n=10000, ε0=4.444](<https://www.sota2.com/research/sota/privacy-budget-estimation-on-shuffled-mechanisms-n-10000-0-4-444.md>): Privacy budget estimation; Shuffled Mechanisms n=10000, ε0=4.444; Privacy Budget (Epsilon): 0.4.

- [Privacy Budget Estimation on Shuffled mechanism (n=10000, epsilon\_0=4.444) (test)](<https://www.sota2.com/research/sota/privacy-budget-estimation-on-shuffled-mechanism-n-10000-epsilon_0-4-444-test.md>): Privacy budget estimation; Shuffled mechanism (n=10000, epsilon\_0=4.444) (test); Delta Score: 0.000003.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2310.19973>)

[PDF](<https://arxiv.org/pdf/2310.19973.pdf>)