The Pseudo-Dimension of Near-Optimal Auctions

TL;DR

This paper introduces $t$-level auctions, a flexible class that balances simplicity and expressivity, and proves they can be learned efficiently with near-optimal revenue guarantees using statistical learning theory.

Contribution

The paper develops a new class of $t$-level auctions and analyzes their pseudo-dimension, enabling efficient learning of near-optimal auctions from data.

Findings

$t$-level auctions have small representation error.

The pseudo-dimension of $t$-level auctions is modest for polynomial $t$.

Near-optimal revenue can be learned from polynomially many samples.

Abstract

This paper develops a general approach, rooted in statistical learning theory, to learning an approximately revenue-maximizing auction from data. We introduce $t$-level auctions to interpolate between simple auctions, such as welfare maximization with reserve prices, and optimal auctions, thereby balancing the competing demands of expressivity and simplicity. We prove that such auctions have small representation error, in the sense that for every product distribution $F$ over bidders' valuations, there exists a $t$-level auction with small $t$ and expected revenue close to optimal. We show that the set of $t$-level auctions has modest pseudo-dimension (for polynomial $t$) and therefore leads to small learning error. One consequence of our results is that, in arbitrary single-parameter settings, one can learn a mechanism with expected revenue arbitrarily close to optimal from a polynomial number of samples.