Individualized Privacy Accounting via Subsampling with Applications in Combinatorial Optimization

TL;DR

This paper introduces a new privacy accounting technique that leverages subsampling to convert one-sided add-DP algorithms into two-sided DP algorithms, leading to improved private algorithms for combinatorial optimization and streaming problems.

Contribution

The paper presents a novel analysis method for individualized privacy accounting that enhances privacy guarantees and algorithm performance in combinatorial optimization and streaming tasks.

Findings

Improved algorithms for private combinatorial optimization with tight error bounds.

A pure-DP algorithm for the shifting heavy hitter problem in streaming data.

The technique converts one-sided add-DP algorithms into two-sided DP algorithms via subsampling.

Abstract

In this work, we give a new technique for analyzing individualized privacy accounting via the following simple observation: if an algorithm is one-sided add-DP, then its subsampled variant satisfies two-sided DP. From this, we obtain several improved algorithms for private combinatorial optimization problems, including decomposable submodular maximization and set cover. Our error guarantees are asymptotically tight and our algorithm satisfies pure-DP while previously known algorithms (Gupta et al., 2010; Chaturvedi et al., 2021) are approximate-DP. We also show an application of our technique beyond combinatorial optimization by giving a pure-DP algorithm for the shifting heavy hitter problem in a stream; previously, only an approximateDP algorithm was known (Kaplan et al., 2021; Cohen & Lyu, 2023).