# Sequential Experiment Design for Hypothesis Verification

## TL;DR

This paper formulates the hypothesis verification problem as a POMDP and proposes a heuristic strategy that improves confidence levels in hypothesis testing, with demonstrated advantages over existing methods.

## Contribution

It introduces a novel POMDP-based framework for hypothesis verification and proposes a simple heuristic strategy with a game-theoretic interpretation.

## Key findings

- Heuristic strategy outperforms some existing methods in numerical experiments.
- Verification problem formulated as a Markov Decision Process.
- Relationship between hypothesis testing and verification established.

## Abstract

Hypothesis testing is an important problem with applications in target localization, clinical trials etc. Many active hypothesis testing strategies operate in two phases: an exploration phase and a verification phase. In the exploration phase, selection of experiments is such that a moderate level of confidence on the true hypothesis is achieved. Subsequent experiment design aims at improving the confidence level on this hypothesis to the desired level. In this paper, the focus is on the verification phase. A confidence measure is defined and active hypothesis testing is formulated as a confidence maximization problem in an infinite-horizon average-reward Partially Observable Markov Decision Process (POMDP) setting. The problem of maximizing confidence conditioned on a particular hypothesis is referred to as the hypothesis verification problem. The relationship between hypothesis testing and verification problems is established. The verification problem can be formulated as a Markov Decision Process (MDP). Optimal solutions for the verification MDP are characterized and a simple heuristic adaptive strategy for verification is proposed based on a zero-sum game interpretation of Kullback-Leibler divergences. It is demonstrated through numerical experiments that the heuristic performs better in some scenarios compared to existing methods in literature.