Maximizing Stochastic Monotone Submodular Functions

We study the problem of maximizing a stochastic monotone submodular function with respect to a matroid constraint. Our model can capture the effect of uncertainty in different problems, such as cascade effects in social networks, capital budgeting, sensor placement, etc. We study the adaptivity gap the ratio between the values of optimal adaptive and non-adaptive policies and show that it is equal to e e−1 . This result implies that the benefit of adaptivity is bounded. We also study the myopic policy and show that it is a 1 2 -approximation. Furthermore, when the matroid is uniform, approximation ratio of the myopic policy becomes 1− 1 e which is optimum.