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Abstract: We study the problem of maximizing a stochastic monotone submodular functionwith respect to a matroid constraint. Due to the presence of diminishingmarginal values in real-world problems, our model can capture the effect ofstochasticity in a wide range of applications. We show that the adaptivity gap- the ratio between the values of optimal adaptive and optimal non-adaptivepolicies - is bounded and is equal to e-e-1. We propose a polynomial-timenon-adaptive policy that achieves this bound. We also present an adaptivemyopic policy that obtains at least half of the optimal value. Furthermore,when the matroid is uniform, the myopic policy achieves the optimalapproximation ratio of 1-1-e.



Author: Arash Asadpour, Hamid Nazerzadeh

Source: https://arxiv.org/







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