We consider the maximization of a submodular objective function $f:2^U\to\mathbb{R}_{\geq 0}$, where the objective $f$ is not accessed as a value oracle but instead subject to noisy queries. We introduce a versatile adaptive sampling procedure called which determines whether the marginal gain of the function $f$ is approximately above or below an input threshold with high probability in as few noisy samples as possible. Using the sampling procedure as a subroutine, we propose sample efficient algorithms for monotone submodular maximization with cardinality and matroid constraints, as well as unconstrained non-monotone submodular maximization. The proposed algorithms achieve approximation guarantees arbitrarily close to those of the standard value oracle setting. We further provide an experimental evaluation on real instances of submodular maximization and demonstrate the sample efficiency of our proposed algorithm relative to alternative approaches.

翻译：我们考虑子模目标函数 $f:2^U\to\mathbb{R}_{\geq 0}$ 的最大化问题，其中目标函数 $f$ 并非通过取值预言机访问，而是受到带噪查询的影响。我们引入一种自适应采样过程，该过程能够在尽可能少的带噪样本下，以高概率判定函数 $f$ 的边际增益是否近似高于或低于输入阈值。以该采样过程为子程序，我们针对带有基数约束和拟阵约束的单调子模最大化问题，以及无约束非单调子模最大化问题，提出了样本高效的算法。所提算法可达到任意接近标准取值预言机设定下的近似保证。我们进一步在真实子模最大化实例上进行实验评估，证明了所提算法相对于其他方法的样本高效性。