Selling Data To a Machine Learner: Pricing via Costly Signaling

Junjie Chen, Minming Li, Haifeng Xu
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:3336-3359, 2022.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-chen22m, title = {Selling Data To a Machine Learner: Pricing via Costly Signaling}, author = {Chen, Junjie and Li, Minming and Xu, Haifeng}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {3336--3359}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/chen22m/chen22m.pdf}, url = {https://proceedings.mlr.press/v162/chen22m.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Selling Data To a Machine Learner: Pricing via Costly Signaling %A Junjie Chen %A Minming Li %A Haifeng Xu %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-chen22m %I PMLR %P 3336--3359 %U https://proceedings.mlr.press/v162/chen22m.html %V 162 %X 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.
APA
Chen, J., Li, M. & Xu, H.. (2022). Selling Data To a Machine Learner: Pricing via Costly Signaling. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:3336-3359 Available from https://proceedings.mlr.press/v162/chen22m.html.

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