Robust guarantees of stochastic greedy algorithms

Avinatan Hassidim, Yaron Singer

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations


In this paper we analyze the robustness of stochastic variants of the greedy algorithm for submodular maximization. Our main result shows that for maximizing a monotone submodular function under a cardinality constraint, itera-tively selecting an element whose marginal contribution is approximately maximal in expectation is a sufficient condition to obtain the optimal approximation guarantee with exponentially high probability, assuming the cardinality is sufficiently large. One consequence of our result is that the linear-time STOCHASTIC-GREEDY algorithm recently proposed in (Mirzasolciman et al., 2015) achieves the optimal running time while maintaining an optimal approximation guarantee. We also show that high probability guarantees cannot be obtained for stochastic greedy algorithms under matroid constraints, and prove an approximation guarantee which holds in expectation. In contrast to the guarantees of the greedy algorithm, we show that the approximation ratio of stochastic local search is arbitrarily bad, with high probability, as well as in expectation.

Original languageEnglish
Title of host publication34th International Conference on Machine Learning, ICML 2017
PublisherInternational Machine Learning Society (IMLS)
Number of pages9
ISBN (Electronic)9781510855144
StatePublished - 2017
Event34th International Conference on Machine Learning, ICML 2017 - Sydney, Australia
Duration: 6 Aug 201711 Aug 2017

Publication series

Name34th International Conference on Machine Learning, ICML 2017


Conference34th International Conference on Machine Learning, ICML 2017

Bibliographical note

Publisher Copyright:
Copyright 2017 by the author(s).


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