摘要翻译:
离散优化中的许多重要问题都要求在拟阵约束下求单调子模函数的极大值。对于这些问题,一个简单的贪心算法保证得到接近最优解。在本文中,我们将这一经典结果推广到一类部分可观测的自适应优化问题,其中每个选择都依赖于过去选择的观测结果。具体地,我们证明了自然自适应贪婪算法对具有$P$拟阵约束的自适应单调子模函数的最大化问题提供了$1/(P+1)$逼近,更一般地,在任意$P$无关系统上也是如此。我们在一个复杂的自适应匹配应用中说明了我们的结果的有用性。
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英文标题:
《Adaptive Submodular Optimization under Matroid Constraints》
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作者:
Daniel Golovin and Andreas Krause
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最新提交年份:
2011
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分类信息:
一级分类:Computer Science 计算机科学
二级分类:Data Structures and Algorithms 数据结构与算法
分类描述:Covers data structures and analysis of algorithms. Roughly includes material in ACM Subject Classes E.1, E.2, F.2.1, and F.2.2.
涵盖数据结构和算法分析。大致包括ACM学科类E.1、E.2、F.2.1和F.2.2中的材料。
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一级分类:Computer Science 计算机科学
二级分类:Artificial Intelligence 人工智能
分类描述:Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域,除了视觉、机器人、机器学习、多智能体系统以及计算和语言(自然语言处理),这些领域有独立的学科领域。特别地,包括专家系统,定理证明(尽管这可能与计算机科学中的逻辑重叠),知识表示,规划,和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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英文摘要:
Many important problems in discrete optimization require maximization of a monotonic submodular function subject to matroid constraints. For these problems, a simple greedy algorithm is guaranteed to obtain near-optimal solutions. In this article, we extend this classic result to a general class of adaptive optimization problems under partial observability, where each choice can depend on observations resulting from past choices. Specifically, we prove that a natural adaptive greedy algorithm provides a $1/(p+1)$ approximation for the problem of maximizing an adaptive monotone submodular function subject to $p$ matroid constraints, and more generally over arbitrary $p$-independence systems. We illustrate the usefulness of our result on a complex adaptive match-making application.
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PDF链接:
https://arxiv.org/pdf/1101.4450