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DOI: 10.4230/LIPIcs.ITCS.2023.75

Learning Reserve Prices in Second-Price Auctions

Authors: Yaonan Jin, Pinyan Lu, and Tao Xiao

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract

This paper proves the tight sample complexity of Second-Price Auction with Anonymous Reserve, up to a logarithmic factor, for each of all the value distribution families studied in the literature: [0,1]-bounded, [1,H]-bounded, regular, and monotone hazard rate (MHR). Remarkably, the setting-specific tight sample complexity poly(ε^{-1}) depends on the precision ε ∈ (0, 1), but not on the number of bidders n ≥ 1. Further, in the two bounded-support settings, our learning algorithm allows correlated value distributions. In contrast, the tight sample complexity Θ̃(n) ⋅ poly(ε^{-1}) of Myerson Auction proved by Guo, Huang and Zhang (STOC 2019) has a nearly-linear dependence on n ≥ 1, and holds only for independent value distributions in every setting. We follow a similar framework as the Guo-Huang-Zhang work, but replace their information theoretical arguments with a direct proof.

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Yaonan Jin, Pinyan Lu, and Tao Xiao. Learning Reserve Prices in Second-Price Auctions. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 75:1-75:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{jin_et_al:LIPIcs.ITCS.2023.75,
  author =	{Jin, Yaonan and Lu, Pinyan and Xiao, Tao},
  title =	{{Learning Reserve Prices in Second-Price Auctions}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{75:1--75:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.75},
  URN =		{urn:nbn:de:0030-drops-175780},
  doi =		{10.4230/LIPIcs.ITCS.2023.75},
  annote =	{Keywords: Revenue Maximization, Sample Complexity, Anonymous Reserve}
}

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Learning Reserve Prices in Second-Price Auctions

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