## 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.

Original language | American English |
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Pages (from-to) | 277-291 |

Number of pages | 15 |

Journal | Lecture Notes in Computer Science |

Volume | 8877 |

DOIs | |

State | Published - 2014 |

### Bibliographical note

Publisher Copyright:© Springer International Publishing Switzerland 2014.