arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2011.03030stat.MLcs.LGmath.OCmath.STstat.TH
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上下文线性优化的快速算法

Fast Rates for Contextual Linear Optimization

Cornell University(康奈尔大学)

Yichun Hu, Nathan Kallus, Xiaojie Mao

摘要:

在决策过程中对边观察进行分析可以减少不确定性并提高性能,但这也要求我们处理潜在的复杂预测关系。虽然人们可以使用现成的机器学习方法来单独学习预测模型并将其插入,但各种最近的方法通过拟合模型来集成估计和优化,以直接优化下游决策性能。令人惊讶的是,在上下文线性优化的情况下,我们表明,天真的插件方法实际上实现了后悔收敛速度显着快于直接优化下游决策性能的方法。我们证明了这一点,利用特定的问题实例没有任意坏的近对偶退化的事实。虽然在我们讨论和说明数字时还有其他利弊需要考虑,但我们的结果突出了企业集成估计和优化的细微差别。我们的研究结果总体上对实践是积极的:预测模型使用现有工具进行训练是容易和快速的,解释简单,并且,正如我们所展示的,导致决策表现非常好。

英文摘要:

Incorporating side observations in decision making can reduce uncertainty and boost performance, but it also requires we tackle a potentially complex predictive relationship. While one may use off-the-shelf machine learning methods to separately learn a predictive model and plug it in, a variety of recent methods instead integrate estimation and optimization by fitting the model to directly optimize downstream decision performance. Surprisingly, in the case of contextual linear optimization, we show that the naive plug-in approach actually achieves regret convergence rates that are significantly faster than methods that directly optimize downstream decision performance. We show this by leveraging the fact that specific problem instances do not have arbitrarily bad near-dual-degeneracy. While there are other pros and cons to consider as we discuss and illustrate numerically, our results highlight a nuanced landscape for the enterprise to integrate estimation and optimization. Our results are overall positive for practice: predictive models are easy and fast to train using existing tools, simple to interpret, and, as we show, lead to decisions that perform very well.

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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