Sampling and Representation Complexity of Revenue Maximization

TL;DR

This paper investigates the relationship between the number of samples needed and the complexity of representing approximately revenue-maximizing auctions, providing bounds and lower bounds on these complexities.

Contribution

It establishes tight bounds and an exponential lower bound linking sample complexity to the representation complexity of revenue-maximizing auctions.

Findings

Sample complexity is tightly related to auction representation complexity.

Provided upper bounds on the number of samples needed.

Proved an exponential lower bound on sample complexity.

Abstract

We consider (approximate) revenue maximization in auctions where the distribution on input valuations is given via "black box" access to samples from the distribution. 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.