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.
Fast Adaptive Non-Monotone Submodular Maximization Subject to a Knapsack Constraint / Amanatidis, Georgios; Fusco, Federico; Lazos, Filippos; Leonardi, Stefano; Reiffenhauser, REBECCA EVA MARIA. - In: THE JOURNAL OF ARTIFICIAL INTELLIGENCE RESEARCH. - ISSN 1076-9757. - 74:(2022), pp. 661-690. [10.1613/jair.1.13472]
Fast Adaptive Non-Monotone Submodular Maximization Subject to a Knapsack Constraint
Amanatidis, Georgios
;Fusco, Federico
;Lazos, Filippos
;Leonardi, Stefano
;Reiffenhauser, REBECCA EVA MARIA
2022
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.File | Dimensione | Formato | |
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Note: DOI: https://doi.org/10.1613/jair.1.13472
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