Efficient Empirical Revenue Maximization in Single-Parameter Auction Environments

TL;DR

This paper introduces a polynomial-time algorithm that learns near-optimal revenue-maximizing auctions from samples across various single-parameter auction environments, handling complex and irregular valuation distributions.

Contribution

It provides the first polynomial-time method for approximately maximizing revenue in diverse single-parameter auctions with arbitrary valuation distributions, including complex environments like knapsack.

Findings

Algorithm works with arbitrary bounded distributions

Simplifies analysis using value-space approach

Extends to intractable environments like knapsack

Abstract

We present a polynomial-time algorithm that, given samples from the unknown valuation distribution of each bidder, learns an auction that approximately maximizes the auctioneer's revenue in a variety of single-parameter auction environments including matroid environments, position environments, and the public project environment. The valuation distributions may be arbitrary bounded distributions (in particular, they may be irregular, and may differ for the various bidders), thus resolving a problem left open by previous papers. The analysis uses basic tools, is performed in its entirety in value-space, and simplifies the analysis of previously known results for special cases. Furthermore, the analysis extends to certain single-parameter auction environments where precise revenue maximization is known to be intractable, such as knapsack environments.