Data-Driven Optimal Transport Cost Selection For Distributionally Robust Optimization
Data-Driven Optimal Transport Cost Selection For Distributionally Robust Optimization
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DOI：
10.1109/wsc40007.2019.9004785
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发表时间：
2017-05
期刊：
影响因子：
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通讯作者：
J. Blanchet;Yang Kang;Karthyek Murthy;Fan Zhang
中科院分区：
文献类型：
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作者：
J. Blanchet;Yang Kang;Karthyek Murthy;Fan Zhang
最近的一些工作表明，一些机器学习算法，如平方根Lasso，支持向量机和正则化逻辑回归等，可以精确地表示为分布式鲁棒优化（DRO）问题。分布不确定性集被定义为以经验分布为中心的邻域，该邻域由最优传输距离度量。在本文中，我们提出了一种以自然数据驱动的方式学习这种邻域的方法。我们严格地表明，我们的框架包括自适应正则化作为一个特殊的情况。此外，我们经验证明，我们提出的方法能够改善广泛的流行的机器学习估计。
Some recent works showed that several machine learning algorithms, such as square-root Lasso, Support Vector Machines, and regularized logistic regression, among many others, can be represented exactly as distributionally robust optimization (DRO) problems. The distributional uncertainty set is defined as a neighborhood centered at the empirical distribution, and the neighborhood is measured by optimal transport distance. In this paper, we propose a methodology which learns such neighborhood in a natural data-driven way. We show rigorously that our framework encompasses adaptive regularization as a particular case. Moreover, we demonstrate empirically that our proposed methodology is able to improve upon a wide range of popular machine learning estimators.