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Prophet inequalities made easy: stochastic optimization by pricing nonstochastic inputs

Dütting, Paul, Feldman, Michal, Kesselheim, Thomas and Lucier, Brendan (2020) Prophet inequalities made easy: stochastic optimization by pricing nonstochastic inputs. SIAM Journal on Computing, 49 (3). 540 - 582. ISSN 0097-5397

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Identification Number: 10.1137/20M1323850

Abstract

We present a general framework for stochastic online maximization problems with combinatorial feasibility constraints. The framework establishes prophet inequalities by constructing price-based online approximation algorithms, a natural extension of threshold algorithms for settings beyond binary selection. Our analysis takes the form of an extension theorem: we derive sufficient conditions on prices when all weights are known in advance, then prove that the resulting approxima- tion guarantees extend directly to stochastic settings. Our framework unifies and simplifies much of the existing literature on prophet inequalities and posted price mechanisms and is used to derive new and improved results for combinatorial markets (with and without complements), multidimensional matroids, and sparse packing problems. Finally, we highlight a surprising connection between the smoothness framework for bounding the price of anarchy of mechanisms and our framework, and show that many smooth mechanisms can be recast as posted price mechanisms with comparable performance guarantees.

Item Type: Article
Official URL: https://epubs.siam.org/loi/smjcat
Additional Information: © 2020 Society for Industrial and Applied Mathematics
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Date Deposited: 07 Apr 2020 13:33
Last Modified: 21 Aug 2020 13:39
URI: http://eprints.lse.ac.uk/id/eprint/104025

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