Sampling and representation complexity of revenue maximization

Shaddin Dughmi, L. Han, Noam Nisan

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)277-291
Number of pages15
JournalLecture Notes in Computer Science
StatePublished - 2014

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)


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