Hypothesis Testing with Conditional Queries: Learnability and the Value of Interaction
Model evaluations may fix all tests before observing any responses or select later tests using earlier responses. We study this choice in a conditional-query model on a finite outcome space $\mathcal{X}$ with $|\mathcal{X}|=N$. We first ask which pairs of distribution classes can be reliably distinguished. We then ask how many additional queries are required to match an adaptive tester when all queried events must be fixed in advance. We show that learnability holds if and only if the two classes have positive separation in their pairwise conditional probabilities. When this separation is zero, the optimal worst-case error is exactly $1/2$ at every finite query budget. For any $T$-query a...
| Authors | Zonghuan Xu |
|---|---|
| Primary category | cs.LG |
| Published | 6 August 2026 |
| Last updated at source | 30 September 2026 |
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