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Prophet inequalities made easy: stochastic optimization by pricing non-stochastic input

Dütting, Paul, Feldman, Michal, Kesselheim, Thomas and Lucier, Brendan (2017) Prophet inequalities made easy: stochastic optimization by pricing non-stochastic input. In: Umans, Chris, (ed.) Proceedings of the 58th Annual IEEE Symposium on Foundations of Computer Science. IEEE Computer Society. ISBN 978-1-5386-3464-6

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Identification Number: 10.1109/FOCS.2017.56

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 approximation 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: Book Section
Official URL: http://www.ieee.org/
Additional Information: © 2017 IEEE
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Sets: Departments > Mathematics
Date Deposited: 15 Nov 2017 17:14
Last Modified: 20 May 2019 00:38
URI: http://eprints.lse.ac.uk/id/eprint/85554

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