# Finite-Sample Analysis of Elimination in Active Hypothesis Testing

arXiv: https://arxiv.org/abs/2605.01039 · HTML: https://mlsanity.com/paper/2605.01039/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 22 references that are in the map.
- First posted on arXiv 1 May 2026.

## Builds on (most cited first, 4 of 4)

- [On the Complexity of Best Arm Identification in Multi-Armed Bandit Models](https://mlsanity.com/paper/1407.4443/) (2014)
- [Optimal Best Arm Identification with Fixed Confidence](https://mlsanity.com/paper/1602.04589/) (2016)
- [On Elimination Strategies for Bandit Fixed-Confidence Identification](https://mlsanity.com/paper/2205.10936/) (2022)
- [Greedy Approximation Algorithms for Active Sequential Hypothesis Testing](https://mlsanity.com/paper/2103.04250/) (2021)

## Abstract (arXiv)

A fixed-confidence, finite-sample problem of active hypothesis testing arises in many safety-critical applications. Situated in the context of sequential hypothesis testing, this paper studies the effect of hypothesis elimination on the stopping time. We introduce an elimination-augmented Track-and-Stop algorithm, in which champion-specific active-opponent sets are progressively pruned, and sensing effort is reallocated toward the surviving alternatives. Our analysis derives a non-asymptotic upper bound on the expected stopping time. The gain in finite-sample from elimination appears on the scale of the non-leading term, resulting from tighter tracking and concentration constants on the reduced hypothesis set. Furthermore, we introduce an aggressiveness parameter to modulate the trade-off between faster elimination and weaker confidence guarantee. An experimental study on synthetic Gaussian instances confirms the theoretical predictions.