多臂Bandit过程的最优动力机制
An Optimal Dynamic Mechanism for Multi-Armed Bandit Processes
摘要：
我们考虑的问题，收入最优的动态机制设计的设置，代理人的类型随着时间的推移而演变的功能，他们（公共和私人）的经验，反复拍卖的项目在无限的地平线。这里的一个核心问题是理解环境的哪些自然限制允许设计最优机制（注意，即使在更简单的静态设置中，最优机制也只能在某些限制下表征）。我们提供了一个{ \em结构表征}的自然“可分离的：多臂强盗环境（其中的进化和激励结构的先验类型是解耦的后续经验在一个精确的意义上），动态最优机制设计是可能的。在这里，我们提出了虚拟索引机制，一个最佳的动态机制，它最大化（长期）{ \em虚拟盈余}使用经典的Gittins算法。该机制在考虑到激励措施的情况下，最佳地平衡了勘探和开采。
英文摘要：
We consider the problem of revenue-optimal dynamic mechanism design in settings where agents' types evolve over time as a function of their (both public and private) experience with items that are auctioned repeatedly over an infinite horizon. A central question here is understanding what natural restrictions on the environment permit the design of optimal mechanisms (note that even in the simpler static setting, optimal mechanisms are characterized only under certain restrictions). We provide a {\em structural characterization} of a natural "separable: multi-armed bandit environment (where the evolution and incentive structure of the a-priori type is decoupled from the subsequent experience in a precise sense) where dynamic optimal mechanism design is possible. Here, we present the Virtual Index Mechanism, an optimal dynamic mechanism, which maximizes the (long term) {\em virtual surplus} using the classical Gittins algorithm. The mechanism optimally balances exploration and exploitation, taking incentives into account.
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