Non-Monotone DR-Submodular Function Maximization
Non-Monotone DR-Submodular Function Maximization
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DOI：
10.1609/aaai.v31i1.10653
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发表时间：
2016-12
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通讯作者：
Tasuku Soma;Yuichi Yoshida
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文献类型：
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作者：
Tasuku Soma;Yuichi Yoshida
我们考虑非释放性DR-submodular函数最大化，其中DR-Submodularity（减少返回子模性）是基于整数晶格的函数的伸展，该功能是基于减小的返回属性的概念。机器学习中的许多应用程序无法通过subsodular集合功能捕获。大约O（N/εlog2 B）的运行时间，其中N是接地集的大小，B是坐标的最大值，ε> 0是一个参数。 B上的运行时间呈指数级比自然贪婪的算法要小。大小更快。
We consider non-monotone DR-submodular function maximization, where DR-submodularity (diminishing return submodularity) is an extension of submodularity for functions over the integer lattice based on the concept of the diminishing return property. Maximizing non-monotone DR-submodular functions has many applications in machine learning that cannot be captured by submodular set functions. In this paper, we present a 1/(2+ε)-approximation algorithm with a running time of roughly O(n/ε log2 B), where n is the size of the ground set, B is the maximum value of a coordinate, and ε > 0 is a parameter. The approximation ratio is almost tight and the dependency of running time on B is exponentially smaller than the naive greedy algorithm. Experiments on synthetic and real-world datasets demonstrate that our algorithm outputs almost the best solution compared to other baseline algorithms, whereas its running time is several orders of magnitude faster.