A Bad Arm Existence Checking Problem

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.