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 via viral marketing. The massive instances occurring in modern-day applications can render existing algorithms prohibitively slow. Moreover, frequently those are also inherently stochastic. Focusing on these challenges, we revisit the classic problem maximizing (possibly non-monotone) function subject to knapsack constraint. We present simple randomized greedy algorithm that achieves 5.83-approximation runs O(n log n) time, i.e., at least factor n faster than other state-of-the-art algorithms. versatility our approach allows us further transfer it stochastic version problem. There, obtain (9 + ?)-approximation best adaptive policy, which is first constant approximation for non-monotone objectives. Experimental evaluation showcases their improved performance real synthetic data.