# A Bad Arm Existence Checking Problem

## TL;DR

This paper introduces a new problem called the bad arm existence checking problem, focusing on efficiently determining if any arm exceeds a loss threshold with minimal draws, relevant to diagnosis tasks.

## Contribution

It formalizes the asymmetric structure of the problem and proposes algorithms with proven theoretical and empirical effectiveness for arm selection and stopping.

## Key findings

- Algorithms effectively identify the existence of positive arms.
- The proposed methods outperform baseline approaches.
- Theoretical analysis confirms the algorithms' efficiency.

## Abstract

We study a bad arm existing checking problem in which a player's task is to judge whether a positive arm exists or not among given K arms by drawing as small number of arms as possible. Here, an arm is positive if its expected loss suffered by drawing the arm is at least a given threshold. This problem is a formalization of diagnosis of disease or machine failure. An interesting structure of this problem is the asymmetry of positive and negative (non-positive) arms' roles; finding one positive arm is enough to judge existence while all the arms must be discriminated as negative to judge non-existence. We propose an algorithms with arm selection policy (policy to determine the next arm to draw) and stopping condition (condition to stop drawing arms) utilizing this asymmetric problem structure and prove its effectiveness theoretically and empirically.