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DOI: 10.4230/LIPIcs.ITCS.2020.60

Optimal Single-Choice Prophet Inequalities from Samples

Authors: Aviad Rubinstein, Jack Z. Wang, and S. Matthew Weinberg

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

Abstract

We study the single-choice Prophet Inequality problem when the gambler is given access to samples. We show that the optimal competitive ratio of 1/2 can be achieved with a single sample from each distribution. When the distributions are identical, we show that for any constant ε > 0, O(n) samples from the distribution suffice to achieve the optimal competitive ratio (≈ 0.745) within (1+ε), resolving an open problem of [José R. Correa et al., 2019].

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Aviad Rubinstein, Jack Z. Wang, and S. Matthew Weinberg. Optimal Single-Choice Prophet Inequalities from Samples. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 60:1-60:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{rubinstein_et_al:LIPIcs.ITCS.2020.60,
  author =	{Rubinstein, Aviad and Wang, Jack Z. and Weinberg, S. Matthew},
  title =	{{Optimal Single-Choice Prophet Inequalities from Samples}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{60:1--60:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.60},
  URN =		{urn:nbn:de:0030-drops-117452},
  doi =		{10.4230/LIPIcs.ITCS.2020.60},
  annote =	{Keywords: Online algorithms, Probability, Optimization, Prophet inequalities, Samples, Auctions}
}

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Optimal Single-Choice Prophet Inequalities from Samples

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