Maximizing Stochastic Monotone Submodular Functions

Details Maximizing Stochastic Monotone Submodular Functions Maximizing Stochastic Monotone Submodular Functions

2009-08-19

arxiv.org/abs/0908.2788v1

Mathematics

Optimization and Control

11 pages

Scientific paper

We study the problem of maximizing a stochastic monotone submodular function with respect to a matroid constraint. 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.

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