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

• URL: http://arxiv.org/abs/2007.05014v3
• Date: Mon, 23 Oct 2023 07:33:55 GMT
• Title: Fast Adaptive Non-Monotone Submodular Maximization Subject to a Knapsack Constraint
• Authors: Georgios Amanatidis, Federico Fusco, Philip Lazos, Stefano Leonardi, Rebecca Reiffenh\"auser
• Abstract summary: Constrained submodular problems encompass a variety of applications, including personalized recommendation, team formation, and revenueimation via viral marketing. We present a simple greedy algorithm that achieves a $5.83 randomized approximation and runs in $O(n log n)$ prohibitively time time i.e., at least factor $n$ faster than other state-of-the-art algorithms. There, we obtain a 9-approximation, which is the first constant approximation for non-monotone$ objectives. Experimental evaluation of our algorithms showcases their improved performance on real and synthetic data.
• Score: 13.357957711519134
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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, 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.

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