# Instance-Adaptive Hypothesis Tests with Heterogeneous Agents

arXiv: https://arxiv.org/abs/2510.21178 · HTML: https://mlsanity.com/paper/2510.21178/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 38 references that are in the map.
- First posted on arXiv 24 Oct 2025.

## Builds on (most cited first, 7 of 7)

- [Strategic Classification](https://mlsanity.com/paper/1506.06980/) (2015)
- [Strategic Classification from Revealed Preferences](https://mlsanity.com/paper/1710.07887/) (2017)
- [Strategyproof Linear Regression in High Dimensions](https://mlsanity.com/paper/1805.10693/) (2018)
- [Principal-Agent Hypothesis Testing](https://mlsanity.com/paper/2205.06812/) (2022)
- [Incentive-Theoretic Bayesian Inference for Collaborative Science](https://mlsanity.com/paper/2307.03748/) (2023)
- [Sharp Results for Hypothesis Testing with Risk-Sensitive Agents](https://mlsanity.com/paper/2412.16452/) (2024)
- [Critical Values Robust to P-hacking](https://mlsanity.com/paper/2005.04141/) (2020)

## Built on by (most cited first, 3 of 3)

- [Strategic Candidacy in Generative AI Arenas](https://mlsanity.com/paper/2603.26891/) (2026)
- [Optimizing Social Utility in Sequential Experiments](https://mlsanity.com/paper/2605.06520/) (2026)
- [Incentive Alignment in Online Experimentation](https://mlsanity.com/paper/2610.05922/) (2026)

## Abstract (arXiv)

We study hypothesis testing over a heterogeneous population of strategic agents with private information. Any single test applied uniformly across the population yields statistical error that is sub-optimal relative to the performance of an oracle given access to the private information. We show how it is possible to design menus of statistical contracts that pair type-optimal tests with payoff structures, inducing agents to self-select according to their private information. This separating menu elicits agent types and enables the principal to match the oracle performance even without a priori knowledge of the agent type. Our main result fully characterizes the collection of all separating menus that are instance-adaptive, matching oracle performance for an arbitrary population of heterogeneous agents. We identify designs where information elicitation is essentially costless, requiring negligible additional expense relative to a single-test benchmark, while improving statistical performance. Our work establishes a connection between proper scoring rules and menu design, showing how the structure of the hypothesis test constrains the elicitable information. Numerical examples illustrate the geometry of separating menus and the improvements they deliver in error trade-offs. Overall, our results connect statistical decision theory with mechanism design, demonstrating how heterogeneity and strategic participation can be harnessed to improve efficiency in hypothesis testing.