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 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.
2020, Advances in Neural Information Processing Systems 33: Annual Conference on Neural Information Processing Systems 2020,, Pages -
Fast Adaptive Non-Monotone Submodular Maximization Subject to a Knapsack Constraint (04b Atto di convegno in volume)
Georgios Amanatidis, Fusco Federico, Lazos Filippos, Leonardi Stefano, Reiffenhauser Rebecca Eva Maria
Gruppo di ricerca: Algorithms and Data Science