Maximizing expected utility over a knapsack constraint

The expected utility knapsack problem is to pick a set of items with random values so as to maximize the expected utility of the total value of the items picked subject to a knapsack constraint. We devise an approximation algorithm for this problem by combining sample average approximation and greedy submodular maximization. Our main result is an algorithm that maximizes an increasing submodular function over a knapsack constraint with an approximation ratio better than the well known (1−1/e1−1/e) factor.