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arXiv · 2605.01039

Finite-Sample Analysis of Elimination in Active Hypothesis Testing

Ziyuan Lin·Hoang Ngoc Nguyen·Jie Xu·Ivan Ruchkin
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Abstract

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.

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Ziyuan Lin, Hoang Ngoc Nguyen, Jie Xu, Ivan Ruchkin. 2026-05-01. Finite-Sample Analysis of Elimination in Active Hypothesis Testing. https://arxiv.org/abs/2605.01039

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