Finite-Sample Analysis of Elimination in Active Hypothesis Testing

TL;DR

This paper analyzes how hypothesis elimination affects stopping time in active hypothesis testing, introducing an algorithm that prunes hypotheses to improve finite-sample efficiency and balancing elimination speed with confidence guarantees.

Contribution

It proposes an elimination-augmented Track-and-Stop algorithm with non-asymptotic bounds and an aggressiveness parameter for improved finite-sample performance.

Findings

Non-asymptotic upper bound on expected stopping time derived.

Elimination improves finite-sample efficiency on synthetic Gaussian instances.

Aggressiveness parameter balances elimination speed and confidence.

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.