标题： 如何最优地出售高维数据 显示英文标题

标题： How to Sell High-Dimensional Data Optimally

摘要： 受销售大型专有数据问题的启发，我们考虑了Bergemann等人提出的涉及决策买家和垄断卖家的信息定价问题。卖家可以获取决定买家可能采取的各种行动效用的世界状态。由于买家通过更准确的状态评估做出更好的决策而获得更大的效用，因此卖家可以向买家承诺以一定价格提供补充信息。为了应对卖家可能并不完全了解买家的私人偏好（或效用）这一事实，我们将设计数据产品的过程框架化为卖家设计一个收益最大化的统计实验菜单的问题。Cai等人之前的的工作表明，可以在状态空间的多项式时间内找到最优菜单，而我们观察到状态空间在数据维度上是自然指数级的。我们提出了一种算法，仅需要对状态空间进行采样访问，就能保证生成一个与状态空间大小无关的近似最优菜单。然后我们分析了一个高维高斯数据的特例，证明了（a）只需考虑标量高斯实验，（b）可以通过半定规划高效找到此类实验的最优菜单，以及（c）当且仅当买家潜在偏好的集合上满足一个自然分离条件时，才会发生完全剩余提取。 显示英文摘要

摘要： Motivated by the problem of selling large, proprietary data, we consider an information pricing problem proposed by Bergemann et al. that involves a decision-making buyer and a monopolistic seller. The seller has access to the underlying state of the world that determines the utility of the various actions the buyer may take. Since the buyer gains greater utility through better decisions resulting from more accurate assessments of the state, the seller can therefore promise the buyer supplemental information at a price. To contend with the fact that the seller may not be perfectly informed about the buyer's private preferences (or utility), we frame the problem of designing a data product as one where the seller designs a revenue-maximizing menu of statistical experiments. Prior work by Cai et al. showed that an optimal menu can be found in time polynomial in the state space, whereas we observe that the state space is naturally exponential in the dimension of the data. We propose an algorithm which, given only sampling access to the state space, provably generates a near-optimal menu with a number of samples independent of the state space. We then analyze a special case of high-dimensional Gaussian data, showing that (a) it suffices to consider scalar Gaussian experiments, (b) the optimal menu of such experiments can be found efficiently via a semidefinite program, and (c) full surplus extraction occurs if and only if a natural separation condition holds on the set of potential preferences of the buyer.