DP-SPRT: Differentially Private Sequential Probability Ratio Tests

TL;DR

This paper introduces DP-SPRT, a differentially private sequential testing method that improves privacy-utility trade-offs, achieves near-optimal sample complexity, and demonstrates strong practical performance.

Contribution

It proposes DP-SPRT, a novel private sequential test that enhances privacy efficiency and provides theoretical guarantees and practical validation.

Findings

DP-SPRT achieves a factor-of-2 privacy improvement over naive methods.

It provides upper bounds on error and sample complexity for various noise distributions.

Experimental results show DP-SPRT performs well in practice.

Abstract

We revisit Wald's celebrated Sequential Probability Ratio Test for sequential tests of two simple hypotheses, under privacy constraints. We propose DP-SPRT, a wrapper that can be calibrated to achieve desired error probabilities and privacy constraints, addressing a significant gap in previous work. DP-SPRT relies on a private mechanism that processes a sequence of queries and stops after privately determining when the query results fall outside a predefined interval. This OutsideInterval mechanism improves upon naive composition of existing techniques like AboveThreshold, achieving a factor-of-2 privacy improvement and thus potentially benefiting other continual monitoring procedures. We prove generic upper bounds on the error and sample complexity of DP-SPRT that can accommodate various noise distributions based on the practitioner's privacy needs. We exemplify them in two settings: Laplace noise (pure Differential Privacy) and Gaussian noise (R\'enyi differential privacy). In the former setting, by providing a lower bound on the sample complexity of any $\varepsilon$-DP test with prescribed type I and type II errors, we show that DP-SPRT is near optimal when both errors are small and the two hypotheses are close. Moreover, we conduct an experimental study revealing its good practical performance.