论文标题
Wasserstein分布鲁棒优化的正则化
Regularization for Wasserstein Distributionally Robust Optimization
论文作者
论文摘要
最近，最佳运输被证明是需要比较概率度量的各种机器学习应用程序中的有用工具。其中，分布强劲优化的应用自然涉及瓦斯汀的距离，在其不确定性模型，捕获数据移位或最坏情况的情况下。受到瓦斯恒星距离在最佳运输中的正则化成功的启发，我们在本文中研究了Wasserstein分布在强大的优化方面的正则化。首先，我们得出了正规化瓦斯汀分布在鲁棒问题上的一般二元性结果。其次，在熵正则化的情况下，我们完善了这种双重性结果，并在正则化参数消失时提供近似结果。
Optimal transport has recently proved to be a useful tool in various machine learning applications needing comparisons of probability measures. Among these, applications of distributionally robust optimization naturally involve Wasserstein distances in their models of uncertainty, capturing data shifts or worst-case scenarios. Inspired by the success of the regularization of Wasserstein distances in optimal transport, we study in this paper the regularization of Wasserstein distributionally robust optimization. First, we derive a general strong duality result of regularized Wasserstein distributionally robust problems. Second, we refine this duality result in the case of entropic regularization and provide an approximation result when the regularization parameters vanish.
