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. Mo...

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Published in:The Journal of artificial intelligence research Vol. 74; pp. 661 - 690
Main Authors: Amanatidis, Georgios, Fusco, Federico, Lazos, Philip, Leonardi, Stefano, Reiffenhäuser, Rebecca
Format: Journal Article
Language:English
Published: San Francisco AI Access Foundation 01.01.2022
Subjects:
Approximation
Artificial intelligence
Constraints
Greedy algorithms
Mathematical analysis
Maximization
Optimization
ISSN:1076-9757, 1076-9757, 1943-5037
Online Access:Get full text
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Abstract 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. Moreover, 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 versatility of our approach allows us to further transfer it to a stochastic version of the problem. There, we obtain a (9 + ε)-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.
AbstractList 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. Moreover, 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 versatility of our approach allows us to further transfer it to a stochastic version of the problem. There, we obtain a (9 + ε)-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.
Author Leonardi, Stefano
Amanatidis, Georgios
Reiffenhäuser, Rebecca
Fusco, Federico
Lazos, Philip
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crossref_primary_10_1109_TETCI_2023_3306362
crossref_primary_10_1016_j_orl_2025_107295
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SubjectTerms Approximation
Artificial intelligence
Constraints
Greedy algorithms
Mathematical analysis
Maximization
Optimization
Title Fast Adaptive Non-Monotone Submodular Maximization Subject to a Knapsack Constraint
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