Streaming Submodular Maximization with Differential Privacy

TL;DR

This paper addresses the challenge of privately maximizing decomposable submodular functions in streaming data settings, proposing new methods that improve privacy-utility trade-offs and validating them through experiments.

Contribution

It introduces fundamental differentially private baselines for streaming submodular maximization and improves trade-offs specifically for decomposable functions, with theoretical and experimental validation.

Findings

Established baseline methods for private streaming submodular maximization.

Derived improved privacy-utility trade-offs for decomposable functions.

Validated approaches through experimental results.

Abstract

In this work, we study the problem of privately maximizing a submodular function in the streaming setting. Extensive work has been done on privately maximizing submodular functions in the general case when the function depends upon the private data of individuals. However, when the size of the data stream drawn from the domain of the objective function is large or arrives very fast, one must privately optimize the objective within the constraints of the streaming setting. We establish fundamental differentially private baselines for this problem and then derive better trade-offs between privacy and utility for the special case of decomposable submodular functions. A submodular function is decomposable when it can be written as a sum of submodular functions; this structure arises naturally when each summand function models the utility of an individual and the goal is to study the total utility of the whole population as in the well-known Combinatorial Public Projects Problem. Finally, we complement our theoretical analysis with experimental corroboration.