Worst-Case Optimal Multi-Armed Gaussian Best Arm Identification with a Fixed Budget
固定预算下高斯多臂最优臂识别的最坏情形最优性AI 解读 ↓
← 返回论文列表与筛选
阅读说明
本页整理公开书目信息，不生成学术质量评分。AI 解读根据题名及所注明的摘要或原文片段生成，未完成全文核验，可能有误；具体假设、证明与结论请核对原文。摘要保留来源文本，未经模型改写。
DOI 首次登记不等于接收或发表日期。部分更正、评论等条目没有独立摘要；缺少可靠材料时保留待补状态。
本页为预印本版本；arXiv 收录、作者填写的期刊信息以及作者既有发表经历，都不单独证明本篇已接收。作者发表记录按 OpenAlex 身份与完整姓名、本站覆盖期刊 ISSN 及正式卷期核对，只展示已核实例，档案仍可能误合并。
引用量采用 OpenAlex 单条关联记录，不合计多个记录；关联记录可能包含正式发表版本，不等于此版本单独引用。缺失不视为零，引用指标不代表论文质量。
关注作者按书目中的完整姓名匹配，同名和姓名变体需人工辨别。相关论文先按共享细分方向和具体方法排列，再参考通用方法与发表日期。
分类依据与纠错
AI 根据所提供的论文材料归类：摘要研究高斯多臂实验分配与最优臂识别，未明确对应所列领域中的因果识别或离散选择模型。
反馈分类问题
正在核对关联版本…
代码、数据与补充材料
正在核对对应版本的资源…
关注这篇论文的作者
固定预算下高斯多臂最优臂识别的最坏情形最优性
- 研究问题
- 在实验轮数固定、各臂结果服从异方差高斯分布时，如何分配样本以识别均值最高的臂，并刻画最坏情形误判下界？
- 方法与思路
- 作者先分析分布信息对误判概率下界的影响，再在均值与最优臂未知、方差已知的设置下提出广义 Neyman 分配策略。
- 材料陈述的贡献
- 摘要称，最坏情形下界仅依赖结果方差；当样本量增大且最优臂与其他臂的均值差趋于共同值时，所提策略渐近达到下界。
- 阅读关注点
- 应核对最坏情形的参数集合、误判下界的表达式、已知方差的作用，以及均值差趋同条件下渐近最优性的具体含义。
- 阅读边界
- 所给版本为 arXiv 预印本，同行评审及接收状态未核实；摘要中的最优性有特定渐近条件，不能推广为未知方差或有限样本保证。
原文摘要
This study investigates the experimental design problem for identifying the arm with the highest expected outcome, referred to as best arm identification (BAI). In our experiments, the number of treatment-allocation rounds is fixed. During each round, a decision-maker allocates an arm and observes a corresponding outcome, which follows a Gaussian distribution with variances that can differ among the arms. At the end of the experiment, the decision-maker recommends one of the arms as an estimate of the best arm. To design an experiment, we first discuss lower bounds for the probability of misidentification. Our analysis highlights that the available information on the outcome distribution, such as means (expected outcomes), variances, and the choice of the best arm, significantly influences the lower bounds. Because available information is limited in actual experiments, we develop a lower bound that is valid under the unknown means and the unknown choice of the best arm, which are referred to as the worst-case lower bound. We demonstrate that the worst-case lower bound depends solely on the variances of the outcomes. Then, under the assumption that the variances are known, we propose the Generalized-Neyman-Allocation (GNA)-empirical-best-arm (EBA) strategy, an extension of the Neyman allocation proposed by Neyman (1934). We show that the GNA-EBA strategy is asymptotically optimal in the sense that its probability of misidentification aligns with the lower bounds as the sample size increases infinitely and the differences between the expected outcomes of the best and other suboptimal arms converge to the same values across arms. We refer to such strategies as asymptotically worst-case optimal.