# Active Hypothesis Testing: Beyond Chernoff-Stein

## TL;DR

This paper formulates an active hypothesis testing problem allowing a fixed number of experiments and inconclusive decisions, deriving bounds on misclassification probability and proposing a heuristic strategy for optimal decision-making.

## Contribution

It introduces a new active hypothesis testing framework with bounds on misclassification, extending the Chernoff-Stein lemma and proposing a heuristic strategy.

## Key findings

- Derived asymptotically tight bounds on misclassification probability.
- Formulated a generalized Chernoff-Stein lemma for the problem.
- Proposed a heuristic strategy with analyzed performance.

## Abstract

An active hypothesis testing problem is formulated. In this problem, the agent can perform a fixed number of experiments and then decide on one of the hypotheses. The agent is also allowed to declare its experiments inconclusive if needed. The objective is to minimize the probability of making an incorrect inference (misclassification probability) while ensuring that the true hypothesis is declared conclusively with moderately high probability. For this problem, lower and upper bounds on the optimal misclassification probability are derived and these bounds are shown to be asymptotically tight. In the analysis, a sub-problem, which can be viewed as a generalization of the Chernoff-Stein lemma, is formulated and analyzed. A heuristic approach to strategy design is proposed and its relationship with existing heuristic strategies is discussed.