2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS) (2017)
Berkeley, California, USA
Oct. 15, 2017 to Oct. 17, 2017
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/FOCS.2017.56
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), multi-dimensional 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.
approximation theory, combinatorial mathematics, optimisation, pricing, stochastic processes
P. Duetting, M. Feldman, T. Kesselheim and B. Lucier, "Prophet Inequalities Made Easy: Stochastic Optimization by Pricing Non-Stochastic Inputs," 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS), Berkeley, California, USA, 2017, pp. 540-551.