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

• 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
• DOI: 10.1613/jair.1.13472

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.