Finite-Sample Analysis of Elimination in Active Hypothesis Testing
For safety-critical applications requiring fixed-confidence sequential testing, this work provides a theoretically grounded method to reduce stopping time through hypothesis elimination, though the improvement is incremental.
The paper introduces an elimination-augmented Track-and-Stop algorithm for active hypothesis testing that progressively prunes hypothesis sets and reallocates sensing effort, deriving a non-asymptotic upper bound on expected stopping time that shows finite-sample gains from elimination on the scale of non-leading terms.
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.