# DP-SPRT: Differentially Private Sequential Probability Ratio Tests

arXiv: https://arxiv.org/abs/2508.06377 · HTML: https://mlsanity.com/paper/2508.06377/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 36 references that are in the map.
- First posted on arXiv 8 Aug 2025.

## Builds on (most cited first, 19 of 19)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Renyi Differential Privacy](https://mlsanity.com/paper/1702.07476/) (2017)
- [Optimal Best Arm Identification with Fixed Confidence](https://mlsanity.com/paper/1602.04589/) (2016)
- [Hyperparameter Tuning with Renyi Differential Privacy](https://mlsanity.com/paper/2110.03620/) (2021)
- [Explore First, Exploit Next: The True Shape of Regret in Bandit Problems](https://mlsanity.com/paper/1602.07182/) (2016)
- [Composition of Differential Privacy & Privacy Amplification by Subsampling](https://mlsanity.com/paper/2210.00597/) (2022)
- [An Optimal Private Stochastic-MAB Algorithm Based on an Optimal Private Stopping Rule](https://mlsanity.com/paper/1905.09383/) (2019)
- [A Private and Computationally-Efficient Estimator for Unbounded Gaussians](https://mlsanity.com/paper/2111.04609/) (2021)
- [The Structure of Optimal Private Tests for Simple Hypotheses](https://mlsanity.com/paper/1811.11148/) (2018)
- [Differentially Private Chi-Squared Hypothesis Testing: Goodness of Fit and Independence Testing](https://mlsanity.com/paper/1602.03090/) (2016)
- [Near Instance-Optimal PAC Reinforcement Learning for Deterministic MDPs](https://mlsanity.com/paper/2203.09251/) (2022)
- [Differentially Private Nonparametric Hypothesis Testing](https://mlsanity.com/paper/1903.09364/) (2019)
- [Quantile Multi-Armed Bandits: Optimal Best-Arm Identification and a Differentially Private Scheme](https://mlsanity.com/paper/2006.06792/) (2020)
- [The Test of Tests: A Framework For Differentially Private Hypothesis Testing](https://mlsanity.com/paper/2302.04260/) (2023)
- [The Sparse Vector Technique, Revisited](https://mlsanity.com/paper/2010.00917/) (2020)
- [On the Complexity of Differentially Private Best-Arm Identification with Fixed Confidence](https://mlsanity.com/paper/2309.02202/) (2023)
- [Differentially Private Best-Arm Identification](https://mlsanity.com/paper/2406.06408/) (2024)
- [Differentially Private Algorithms for Statistical Verification of Cyber-Physical Systems](https://mlsanity.com/paper/2004.00275/) (2020)
- [Private Sequential Hypothesis Testing for Statisticians: Privacy, Error Rates, and Sample Size](https://mlsanity.com/paper/2204.04597/) (2022)

## Built on by (most cited first, 1 of 1)

- [Optimal Rates for Differentially Private Hypothesis Testing with E-values](https://mlsanity.com/paper/2605.28952/) (2026)

## Abstract (arXiv)

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.