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].
@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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