Finite-Sample Analysis of Elimination in Active Hypothesis Testing

arXiv cs.LG / 5/5/2026

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Key Points

The paper studies a fixed-confidence, finite-sample formulation of active hypothesis testing under sequential settings, focusing on how eliminating hypotheses affects the stopping time.
It proposes an elimination-augmented Track-and-Stop algorithm that prunes champion-specific active opponent sets over time and reallocates sensing effort to the remaining hypotheses.
The authors derive a non-asymptotic upper bound on the expected stopping time, showing that elimination improves performance through tighter tracking and concentration bounds on the reduced hypothesis set.
They introduce an aggressiveness parameter to balance faster hypothesis elimination against maintaining the confidence guarantee.
Experiments on synthetic Gaussian instances validate the theoretical predictions about the finite-sample benefits of elimination.

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.