We study a bad arm existence checking problem in a stochastic K -armed bandit setting, in which a player’s task is to judge whether a positive arm exists or all the arms are negative 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 $$\theta _U$$ θ U , and it is negative if that is less than another given threshold $$\theta _L(\le \theta _U)$$ θ L ( ≤ θ U ) . 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 arms’ roles; finding one positive arm is enough to judge positive existence while all the arms must be discriminated as negative to judge whole negativity. In the case with $$\varDelta =\theta _U-\theta _L>0$$ Δ = θ U - θ L > 0 , we propose elimination algorithms with arm selection policy (policy to determine the next arm to draw) and decision condition (condition to conclude positive arm’s existence or the drawn arm’s negativity) utilizing this asymmetric problem structure and prove its effectiveness theoretically and empirically.

中文翻译：

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一个坏臂存在性检查问题：如何利用非对称问题结构？

我们研究了随机 K 臂老虎机设置中的坏臂存在检查问题，其中玩家的任务是通过绘制尽可能少的臂来判断给定 K 臂中是否存在正臂或所有臂都是负臂。在这里，如果手臂在绘制手臂时遭受的预期损失至少是给定的阈值 $$\theta _U$$ θ U ，则手臂为正，如果小于另一个给定的阈值 $$\theta _L(\ le \theta _U)$$ θ L ( ≤ θ U ) 。这个问题是疾病或机器故障诊断的形式化。这个问题的一个有趣结构是正负臂角色的不对称；找到一个正面的手臂就足以判断正面的存在，而必须将所有手臂都区分为负面来判断整个负面。在 $$\varDelta =\theta _U-\theta _L> 的情况下