标题： 不确定性下的决策制定的吉廷斯指数：一个设计原则 显示英文标题

标题： The Gittins Index: A Design Principle for Decision-Making Under Uncertainty

摘要： Gittins指数是一种能够最优解决各种涉及不确定性的决策问题的工具，包括多臂老虎机问题、减少队列中的平均延迟以及类似“普罗米修斯之盒”模型的搜索问题。 然而，尽管有上述例子以及后来的扩展，Gittins指数能够完美最优求解的问题空间是有限的，与其它多臂老虎机算法相比，其定义更为微妙。 因此，Gittins指数通常被视为一个理论上的重要概念，而不是用于解决决策问题的实际工具。 本教程的目标是展示Gittins指数可以被成功应用于实际问题。 我们首先通过示例来介绍Gittins指数，然后逐步讲解它所解决的几个问题——有些是最佳求解，有些是次优求解但仍然表现出色。 在后一类中，两个实际应用亮点是将Gittins指数应用于贝叶斯优化，以及将Gittins指数应用于减少队列中的尾部延迟。 显示英文摘要

摘要： The Gittins index is a tool that optimally solves a variety of decision-making problems involving uncertainty, including multi-armed bandit problems, minimizing mean latency in queues, and search problems like the Pandora's box model. However, despite the above examples and later extensions thereof, the space of problems that the Gittins index can solve perfectly optimally is limited, and its definition is rather subtle compared to those of other multi-armed bandit algorithms. As a result, the Gittins index is often regarded as being primarily a concept of theoretical importance, rather than a practical tool for solving decision-making problems. The aim of this tutorial is to demonstrate that the Gittins index can be fruitfully applied to practical problems. We start by giving an example-driven introduction to the Gittins index, then walk through several examples of problems it solves - some optimally, some suboptimally but still with excellent performance. Two practical highlights in the latter category are applying the Gittins index to Bayesian optimization, and applying the Gittins index to minimizing tail latency in queues.