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Applying a randomized algorithm to a subset of a dataset rather than theentire dataset is a common approach to amplify its privacy guarantees in thereleased information. We propose a class of subsampling methods namedMUltistage Sampling Technique (MUST) for privacy amplification (PA) in thecontext of differential privacy (DP). We conduct comprehensive analyses of thePA 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 thensampling without (O), with (W), with (W) replacement in stage II from thesubset drawn in stage I. We also provide the privacy composition analysis overrepeated applications of MUST via the Fourier accountant algorithm. Ourtheoretical and empirical results suggest that MUST.OW and MUST.WW havestronger PA in $\epsilon$ than the common one-stage sampling proceduresincluding Poisson sampling, sampling without replacement, and sampling withreplacement, while the results on $\delta$ vary case by case. We also provethat MUST.WO is equivalent to sampling with replacement in PA. Furthermore, thefinal subset generated by a MUST procedure is a multiset that may containmultiple copies of the same data points due to sampling with replacementinvolved, which enhances the computational efficiency of algorithms thatrequire complex function calculations on distinct data points (e.g., gradientdescent). Our utility experiments show that MUST delivers similar or improvedutility and stability in the privacy-preserving outputs compared to one-stagesubsampling methods at similar privacy loss. MUST can be seamlessly integratedinto stochastic optimization algorithms or procedures that involve parallel orsimultaneous subsampling (e.g., bagging and subsampling bootstrap) when DPguarantees are necessary.

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