Abstract
We consider (approximate) revenue maximization in mechanisms where the distribution on input valuations is given via “black box” access to samples from the distribution. We analyze the following model: a single agent, m outcomes, and valuations represented as m-dimensional vectors indexed by the outcomes and drawn from an arbitrary distribution presented as a black box. We observe that the number of samples required – the sample complexity – is tightly related to the representation complexity of an approximately revenue-maximizing auction. Our main results are upper bounds and an exponential lower bound on these complexities. We also observe that the computational task of “learning” a good mechanism from a sample is nontrivial, requiring careful use of regularization in order to avoid over-fitting the mechanism to the sample. We establish preliminary positive and negative results pertaining to the computational complexity of learning a good mechanism for the original distribution by operating on a sample from said distribution.
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Dughmi, S., Han, L., Nisan, N. (2014). Sampling and Representation Complexity of Revenue Maximization. In: Liu, TY., Qi, Q., Ye, Y. (eds) Web and Internet Economics. WINE 2014. Lecture Notes in Computer Science, vol 8877. Springer, Cham. https://doi.org/10.1007/978-3-319-13129-0_22
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DOI: https://doi.org/10.1007/978-3-319-13129-0_22
Publisher Name: Springer, Cham
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