In this paper, we study stochastic submodular maximization problems with general matroid constraints, that naturally arise in online learning, team formation, facility location, influence maximization, active learning and sensing objective functions. In other words, we focus on maximizing submodular functions that are defined as expectations over a class of submodular functions with an unknown distribution. We show that for monotone functions of this form, the stochastic continuous greedy algorithm attains an approximation ratio (in expectation) arbitrarily close to $(1-1/e) \approx 63\%$ using a polynomial estimation of the gradient. We argue that using this polynomial estimator instead of the prior art that uses sampling eliminates a source of randomness and experimentally reduces execution time.

翻译：本文研究了在一般拟阵约束下的随机子模最大化问题，这类问题自然出现在在线学习、团队组建、设施选址、影响力最大化、主动学习和感知目标函数中。换言之，我们关注最大化一类具有未知分布的子模函数期望值的问题。我们证明了对于此类单调函数，通过使用梯度的多项式估计，随机连续贪婪算法能够达到任意接近$(1-1/e) \approx 63\%$的近似比（期望意义下）。我们论证了使用这种多项式估计器替代现有采样方法能够消除随机性来源，并在实验上减少执行时间。