Selling Data To a Machine Learner: Pricing via Costly Signaling

We consider a new problem of selling data to a machine learner who looks to purchase data to train his machine learning model. A key challenge in this setup is that neither the seller nor the machine learner knows the true quality of data. When designing a revenue-maximizing mechanism, a data seller faces the tradeoff between the cost and precision of data quality estimation. To address this challenge, we study a natural class of mechanisms that price data via costly signaling. Motivated by the assumption of i.i.d. data points as in classic machine learning models, we first consider selling homogeneous data and derive an optimal selling mechanism. We then turn to the sale of heterogeneous data, motivated by the sale of multiple data sets, and show that 1) on the negative side, it is NP-hard to approximate the optimal mechanism within a constant ratio e/(e+1) + o(1); while 2) on the positive side, there is a 1/k-approximate algorithm, where k is the number of the machine learner’s private types.