We consider the problem of near-optimal arm identification in the fixed confidence setting of the infinitely armed bandit problem when nothing is known about the arm reservoir distribution. We (1) introduce a PAC-like framework within which to derive and cast results; (2) derive a sample complexity lower bound for near-optimal arm identification; (3) propose an algorithm that identifies a nearly-optimal arm with high probability and derive an upper bound on its sample complexity which is within a log factor of our lower bound; and (4) discuss whether our log^2(1/delta) dependence is inescapable for "two-phase" (select arms first, identify the best later) algorithms in the infinite setting. This work permits the application of bandit models to a broader class of problems where fewer assumptions hold.

考虑在无限臂赌博机问题的固定置信度设置下，当不知道臂储备分布时，近似最优臂识别的问题。我们引入了类 PAC 的框架来推导和表述结果; 推导了近似最优臂识别的样本复杂度下界; 提出了一个算法，以高概率识别出一个接近最优的臂，并推导出其样本复杂度的上界，该上界比我们的下界小一个对数因子；并讨论了我们的 log^2(1/delta) 依赖是否不可避免地适用于无限设置的“两阶段” （先选择臂，后识别最佳）算法。这项工作允许将赌徒模型应用于更广泛的问题类别，其中较少的假设成立。

固定信心下无限臂赌博模型中的纯探索算法