arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1003.3967cs.LGcs.AIcs.DS
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自适应子模块:理论及其在主动学习和随机优化中的应用

Adaptive Submodularity: Theory and Applications in Active Learning and Stochastic Optimization

California Institute of Technology(加州理工学院);ETH Zurich(苏黎世联邦理工学院)

Daniel Golovin, Andreas Krause

摘要:

在部分可观测性下求解随机优化问题,其中需要自适应地做出具有不确定结果的决策,这是一个基本但众所周知的困难挑战。在本文中,我们引入了自适应子模块的概念,推广子模块集函数的自适应政策。我们证明了,如果一个问题满足这一性质,一个简单的自适应贪心算法是保证竞争的最优策略。除了为随机最大化和覆盖提供性能保证之外,还可以利用自适应子模块化通过使用惰性评估来大幅加速贪心算法。我们说明了有用的概念,给出了几个例子,自适应子模块化的目标在不同的应用,包括传感器的位置,病毒式营销和主动学习。证明这些问题的自适应子模块性,使我们能够恢复现有的结果在这些应用中的特殊情况下,提高近似保证和处理自然的推广。

英文摘要:

Solving stochastic optimization problems under partial observability, where one needs to adaptively make decisions with uncertain outcomes, is a fundamental but notoriously difficult challenge. In this paper, we introduce the concept of adaptive submodularity, generalizing submodular set functions to adaptive policies. We prove that if a problem satisfies this property, a simple adaptive greedy algorithm is guaranteed to be competitive with the optimal policy. In addition to providing performance guarantees for both stochastic maximization and coverage, adaptive submodularity can be exploited to drastically speed up the greedy algorithm by using lazy evaluations. We illustrate the usefulness of the concept by giving several examples of adaptive submodular objectives arising in diverse applications including sensor placement, viral marketing and active learning. Proving adaptive submodularity for these problems allows us to recover existing results in these applications as special cases, improve approximation guarantees and handle natural generalizations.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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