论文标题

正式化对运行时分布的偏好

Formalizing Preferences Over Runtime Distributions

论文作者

Graham, Devon R., Leyton-Brown, Kevin, Roughgarden, Tim

论文摘要

在试图解决计算问题时,我们经常面临一个可以保证返回正确答案但运行时分布不同的算法之间的选择(例如,SAT求解器,分类算法)。本文旨在通过对运行时分布的偏好进行正式的偏好来奠​​定理论基础。看来我们应该只喜欢最小化预期运行时的算法。但是,这样的偏好将由我们的算法在不良输入上的速度慢慢驱动,而实际上,我们通常愿意在结束之前偶尔切断偶尔的,足够长的时间。我们提出了一种原则性的替代方案,采用一种实用学理论方法来表征描述偏好比算法的偏好的评分函数。这些功能取决于我们解决问题的价值随着时间的流逝而减少,并取决于绘制Captimes的分布。我们描述了现实的效用函数的示例,并展示了如何利用用于建模未指定的CAPTIME分布的最大渗透方法。最后,我们展示了如何有效地估计算法对运行时样品的预期实用程序。

When trying to solve a computational problem, we are often faced with a choice between algorithms that are guaranteed to return the right answer but differ in their runtime distributions (e.g., SAT solvers, sorting algorithms). This paper aims to lay theoretical foundations for such choices by formalizing preferences over runtime distributions. It might seem that we should simply prefer the algorithm that minimizes expected runtime. However, such preferences would be driven by exactly how slow our algorithm is on bad inputs, whereas in practice we are typically willing to cut off occasional, sufficiently long runs before they finish. We propose a principled alternative, taking a utility-theoretic approach to characterize the scoring functions that describe preferences over algorithms. These functions depend on the way our value for solving our problem decreases with time and on the distribution from which captimes are drawn. We describe examples of realistic utility functions and show how to leverage a maximum-entropy approach for modeling underspecified captime distributions. Finally, we show how to efficiently estimate an algorithm's expected utility from runtime samples.

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