How to Sell High-Dimensional Data Optimally
This addresses the challenge of pricing proprietary data in economics and machine learning, offering incremental improvements in computational efficiency for high-dimensional settings.
The paper tackles the problem of optimally selling high-dimensional data by designing revenue-maximizing menus of statistical experiments for a monopolistic seller, proposing an algorithm that generates near-optimal menus with sample complexity independent of the state space and analyzing a Gaussian case to show efficient computation and conditions for full surplus extraction.
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.