Optimal Rates for Differentially Private Hypothesis Testing with E-values
E-values have attracted considerable interest in recent years as flexible tools for enabling anytime-valid and adaptive data analysis. Hypothesis testing is at the core of many of these applications, which can often involve private or sensitive data. In this work, we answer a simple but important question: given two distributions $\mathbb{P}$ and $\mathbb{Q}$, what is the maximum achievable e-power when testing $X\sim \mathbb{P}^n$ against $X\sim\mathbb{Q}^n$ with e-values that satisfy $\varepsilon$-differential privacy? We characterize the optimal rate for this problem and provide an algorithm which matches it exactly. In the sequential setting, when observations arrive one-by-one and th...
| Authors | Ben Jacobsen, Tomas Gonzalez, Gavin Brown et al. |
|---|---|
| Primary category | cs.CR |
| Published | 27 May 2026 |
| Last updated at source | 29 May 2026 |
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