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Single-Sample Prophet Inequalities via Greedy-Ordered Selection
Conference proceeding   Open access

Single-Sample Prophet Inequalities via Greedy-Ordered Selection

Constantine Caramanis, Paul Dütting, Matthew Faw, Federico Fusco, Philip Lazos, Stefano Leonardi, Orestis Papadigenopoulos, Emmanouil Pountourakis and Rebecca Reiffenhäuser
Proceedings of the 2022 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp 1298-1325
04 Nov 2021
DOI: https://doi.org/10.1137/1.9781611977073.54
url
https://doi.org/10.1137/1.9781611977073.54View
Published, Version of Record (VoR)Open Access (License Unspecified),  Open

Abstract

We study single-sample prophet inequalities (SSPIs), i.e., prophet inequalities where only a single sample from each prior distribution is available. Besides a direct, and optimal, SSPI for the basic single choice problem [Rubinstein et al., 2020], most existing SSPI results were obtained via an elegant, but inherently lossy reduction to order-oblivious secretary (OOS) policies [Azar et al., 2014]. Motivated by this discrepancy, we develop an intuitive and versatile greedy-based technique that yields SSPIs directly rather than through the reduction to OOSs. Our results can be seen as generalizing and unifying a number of existing results in the area of prophet and secretary problems. Our algorithms significantly improve on the competitive guarantees for a number of interesting scenarios (including general matching with edge arrivals, bipartite matching with vertex arrivals, and certain matroids), and capture new settings (such as budget additive combinatorial auctions). Complementing our algorithmic results, we also consider mechanism design variants. Finally, we analyze the power and limitations of different SSPI approaches by providing a partial converse to the reduction from SSPI to OOS given by Azar et al.

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