Enhancing Trade-offs in Privacy, Utility, and Computational Efficiency through MUltistage Sampling Technique (MUST)

Applying a randomized algorithm to a subset of a dataset rather than the entire dataset is a common approach to amplify its privacy guarantees in the released information. We propose a class of subsampling methods named MUltistage Sampling Technique (MUST) for privacy amplification (PA) in the context of differential privacy (DP). We conduct comprehensive analyses of the PA effects and utility for several 2-stage MUST procedures, namely, MUST.WO, MUST.OW, and MUST.WW that respectively represent sampling with (W), without (O), with (W) replacement from the original dataset in stage I and then sampling without (O), with (W), with (W) replacement in stage II from the subset drawn in stage I. We also provide the privacy composition analysis over repeated applications of MUST via the Fourier accountant algorithm. Our theoretical and empirical results suggest that MUST.OW and MUST.WW have stronger PA in $\epsilon$ than the common one-stage sampling procedures including Poisson sampling, sampling without replacement, and sampling with replacement, while the results on $\delta$ vary case by case. We also prove that MUST.WO is equivalent to sampling with replacement in PA. Furthermore, the final subset generated by a MUST procedure is a multiset that may contain multiple copies of the same data points due to sampling with replacement involved, which enhances the computational efficiency of algorithms that require complex function calculations on distinct data points (e.g., gradient descent). Our utility experiments show that MUST delivers similar or improved utility and stability in the privacy-preserving outputs compared to one-stage subsampling methods at similar privacy loss. MUST can be seamlessly integrated into stochastic optimization algorithms or procedures that involve parallel or simultaneous subsampling (e.g., bagging and subsampling bootstrap) when DP guarantees are necessary.