在众多平均数中求最大平均数
On Finding the Largest Mean Among Many
摘要：
从分布中抽样以找到具有最大均值的分布出现在广泛的应用中，并且可以在数学上将其建模为多臂强盗问题，其中每个分布与一个手臂相关联。本文研究了识别最佳手臂的样本复杂性（最大均值）多臂强盗问题。受大规模应用的启发，我们特别感兴趣的是确定的情况下，样本的总数是必要的和足够的，以找到最好的手臂规模与手臂的数量线性。我们提出了一个单参数的多臂强盗模型，跨越范围从线性到超线性的样本复杂性。我们还给出了一个新的算法，最佳臂识别，称为PRISM，线性样本的复杂性为广泛的平均分布。该算法，像大多数多臂土匪的探索程序，是自适应的意义上说，下一个武器的样本是根据以前的样本选择。我们比较样本的自适应程序与简单的非自适应程序使用新的下限的复杂性。对于许多问题实例，非自适应程序所需的增加的样本复杂性是臂数的多项式因子。
英文摘要：
Sampling from distributions to find the one with the largest mean arises in a broad range of applications, and it can be mathematically modeled as a multi-armed bandit problem in which each distribution is associated with an arm. This paper studies the sample complexity of identifying the best arm (largest mean) in a multi-armed bandit problem. Motivated by large-scale applications, we are especially interested in identifying situations where the total number of samples that are necessary and sufficient to find the best arm scale linearly with the number of arms. We present a single-parameter multi-armed bandit model that spans the range from linear to superlinear sample complexity. We also give a new algorithm for best arm identification, called PRISM, with linear sample complexity for a wide range of mean distributions. The algorithm, like most exploration procedures for multi-armed bandits, is adaptive in the sense that the next arms to sample are selected based on previous samples. We compare the sample complexity of adaptive procedures with simpler non-adaptive procedures using new lower bounds. For many problem instances, the increased sample complexity required by non-adaptive procedures is a polynomial factor of the number of arms.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
