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arXiv 1807.09358cs.AIcs.DS
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风险规避次模优化问题的一个近似算法

An Approximation Algorithm for Risk-averse Submodular Optimization

Princeton University(普林斯顿大学)

Lifeng Zhou, Pratap Tokekar

摘要:

研究了在不确定性条件下进行组合决策时引入风险的问题。我们制定了一个离散的子模块最大化问题,选择一组使用条件风险价值(CVaR),金融分析中常用的风险度量。虽然CVaR最近已被用于机器人的线性成本函数的优化,我们采取的第一阶段对扩展到离散子模块优化,并提供了一些积极的结果。具体来说,我们提出了顺序贪心算法,提供了一个近似保证找到最大值的CVaR成本函数下的拟阵约束。近似保证表明,我们的算法所产生的解决方案是在一个恒定的因素的最佳和一个附加项,取决于最佳。我们的分析使用了次模集函数的曲率,并证明了该算法在多项式时间内运行。这公式化了许多出现在机器人学中的组合优化问题。我们使用两个这样的问题,车辆分配的不确定性下的机动性按需和传感器的选择与失败的环境监测,作为案例研究,以证明我们的配方的功效。

英文摘要:

We study the problem of incorporating risk while making combinatorial decisions under uncertainty. We formulate a discrete submodular maximization problem for selecting a set using Conditional-Value-at-Risk (CVaR), a risk metric commonly used in financial analysis. While CVaR has recently been used in optimization of linear cost functions in robotics, we take the first stages towards extending this to discrete submodular optimization and provide several positive results. Specifically, we propose the Sequential Greedy Algorithm that provides an approximation guarantee on finding the maxima of the CVaR cost function under a matroidal constraint. The approximation guarantee shows that the solution produced by our algorithm is within a constant factor of the optimal and an additive term that depends on the optimal. Our analysis uses the curvature of the submodular set function, and proves that the algorithm runs in polynomial time. This formulates a number of combinatorial optimization problems that appear in robotics. We use two such problems, vehicle assignment under uncertainty for mobility-on-demand and sensor selection with failures for environmental monitoring, as case studies to demonstrate the efficacy of our formulation.

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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