Finite-Sample Analysis of Elimination in Active Hypothesis Testing

2026-05-01

AI Summary

This work addresses the problem of optimizing finite-sample stopping times under fixed confidence in active hypothesis testing, with a focus on how hypothesis elimination influences decision efficiency. The authors propose a Track-and-Stop algorithm enhanced with a hypothesis elimination mechanism that dynamically prunes competing hypotheses and reallocates sensing resources to accelerate identification of the true hypothesis. They innovatively quantify, within a finite-sample analysis, the improvement hypothesis elimination brings to non-dominant terms of the stopping time bound and introduce a tunable aggressiveness parameter to balance elimination speed against confidence guarantees. Leveraging techniques from sequential hypothesis testing, adaptive sampling, and concentration inequalities, they derive a non-asymptotic upper bound on the expected stopping time and validate the theoretical predictions through experiments on synthetic Gaussian data.

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.

Problem

• active hypothesis testing
• finite-sample analysis
• hypothesis elimination
• stopping time
• fixed-confidence

Innovation

• active hypothesis testing
• hypothesis elimination
• finite-sample analysis
• Track-and-Stop algorithm
• non-asymptotic bound