Fast Adaptive Non-Monotone Submodular Maximization Subject to a Knapsack Constraint

Constrained submodular maximization problems encompass a wide variety of applications, including personalized recommendation, team formation, and revenue maximization via viral marketing. The massive instances occurring in modern day applications can render existing algorithms prohibitively slow, wh...

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Vydáno v:arXiv.org
Hlavní autoři: Amanatidis, Georgios, Fusco, Federico, Lazos, Philip, Leonardi, Stefano, Reiffenhäuser, Rebecca
Médium: Paper
Jazyk:angličtina
Vydáno: Ithaca Cornell University Library, arXiv.org 23.10.2023
Témata:
Algorithms
Approximation
Constraints
Greedy algorithms
Mathematical analysis
Maximization
Optimization
ISSN:2331-8422
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Shrnutí:Constrained submodular maximization problems encompass a wide variety of applications, including personalized recommendation, team formation, and revenue maximization via viral marketing. The massive instances occurring in modern day applications can render existing algorithms prohibitively slow, while frequently, those instances are also inherently stochastic. Focusing on these challenges, we revisit the classic problem of maximizing a (possibly non-monotone) submodular function subject to a knapsack constraint. We present a simple randomized greedy algorithm that achieves a \(5.83\) approximation and runs in \(O(n \log n)\) time, i.e., at least a factor \(n\) faster than other state-of-the-art algorithms. The robustness of our approach allows us to further transfer it to a stochastic version of the problem. There, we obtain a 9-approximation to the best adaptive policy, which is the first constant approximation for non-monotone objectives. Experimental evaluation of our algorithms showcases their improved performance on real and synthetic data.
Bibliografie:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.2007.05014