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The Pseudo-Dimension of Near-Optimal Auctions
Computer Science and Game Theory · Submitted 11 Jun 2015
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | This paper develops a general approach, rooted in statistical learning theory, to learning an approximately revenue-maximizing auction from data. | contribution 0.98 | 0.94 | 0.10 | asserted 1.00 |
| s1 | 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. | contribution 0.71 | 0.92 | 0.05 | asserted 0.99 |
| s2 | 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. | result 0.98 | 0.92 | 0.16 | asserted 1.00 |
| s3 | We show that the set of $t$-level auctions has modest pseudo-dimension (for polynomial $t$) and therefore leads to small learning error. | result 0.96 | 0.95 | 0.14 | asserted 1.00 |
| s4 | 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. | interpretation 0.90 | 0.90 | 0.67 | asserted 0.90 |
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The paper
Original 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.
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How the literature uses it
4 arXiv papers cite this in 5 sentences
Papers citing it · 2 sentences without a confident label
Cites it as background 3 papers
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Recent work has explored settings of learning approximately optimal auction from samples, both for single-item auctions [ref] , and multi-item auctions [ref] .
Robust Learning of Optimal Auctions · Related work · 0.99
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This work has lead to an almost complete picture for the single-item (and the more general single-parameter) setting where Myerson's theory applies, showing how near-optimal mechanisms can be learned from polynomially many (in the approximation and the number of bidders) samples [ref] .
Learning Multi-item Auctions with (or without) Samples · Introduction · 0.82
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The research in this line has advanced from single-unit auctions [ref] to general single-parametric agents [ref] to multi-parameter unit-demand buyers [ref] .
Double Auctions in Markets for Multiple Kinds of Goods · Random Sampling · 0.85
What it cites
Compares with 1 paper
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Our general positive results obviously cover the bounded-valuation and MHR settings in [ref] , though the specialized analysis in [ref] yields better (indeed, almost optimal) sample complexity bounds, as a function of $^-1$ and/or $H$.
Making the Most of Your Samples · Related Work · 0.98
Cites as background 1 paper
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[ref] consider learning the optimal price from samples when there is a single buyer and a single seller; this problem was also studied implicitly in [ref] .
Making the Most of Your Samples · Related Work · 0.88
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