We study a pair of budget- and performance-constrained weak submodular maximization problems. For computational efficiency, we explore the use of stochastic greedy algorithms which limit the search space via random sampling instead of the standard greedy procedure which explores the entire feasible search space. We propose a pair of stochastic greedy algorithms, namely, Modified Randomized Greedy (MRG) and Dual Randomized Greedy (DRG) to approximately solve the budget- and performance-constrained problems, respectively. For both algorithms, we derive approximation guarantees that hold with high probability. We then examine the use of DRG in robust optimization problems wherein the objective is to maximize the worst-case of a number of weak submodular objectives and propose the Randomized Weak Submodular Saturation Algorithm (Random-WSSA). We further derive a high-probability guarantee for when Random-WSSA successfully constructs a robust solution. Finally, we showcase the effectiveness of these algorithms in a variety of relevant uses within the context of Earth-observing LEO constellations which estimate atmospheric weather conditions and provide Earth coverage.

中文翻译：

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考虑稳健性考虑的弱子模传感器选择的随机贪婪方法


我们研究了一对受预算和性能限制的弱子模最大化问题。为了提高计算效率，我们探索了随机贪婪算法的使用，该算法通过随机抽样来限制搜索空间，而不是探索整个可行搜索空间的标准贪婪过程。我们提出了一对随机贪婪算法，即修正随机贪婪 （MRG） 和双随机贪婪 （DRG），分别近似地解决了预算和性能受限的问题。对于这两种算法，我们推导出了高概率成立的近似保证。然后，我们研究了 DRG 在稳健优化问题中的使用，其中目标是最大化许多弱子模目标的最坏情况，并提出了随机弱子模饱和算法 （Random-WSSA）。我们进一步推导出了 Random-WSSA 成功构建稳健解的高概率保证。最后，我们展示了这些算法在地球观测 LEO 星座的各种相关用途中的有效性，这些星座估计大气天气条件并提供地球覆盖。