论文标题
Tikhonov正则化在Martingale限制下是最佳运输
Tikhonov Regularization is Optimal Transport Robust under Martingale Constraints
论文作者
论文摘要
已显示出强大的优化在分布方面可提供一种规范学习模型的原则方法。在本文中，我们发现Tikhonov的正则化在最佳运输意义上是稳健的（即，如果对手在经验措施的合适最佳运输邻居中选择分布），前提是也强加了适当的Martingale约束。此外，我们介绍了Martingale约束的放松，这不仅为一类现有的强大方法提供了统一的观点，而且还会导致新的正则化工具。为了实现这些新颖的工具，提出了可拖动的计算算法。作为副产品，本文证明的强二元定理可以潜在地应用于其他独立兴趣的问题。
Distributionally robust optimization has been shown to offer a principled way to regularize learning models. In this paper, we find that Tikhonov regularization is distributionally robust in an optimal transport sense (i.e., if an adversary chooses distributions in a suitable optimal transport neighborhood of the empirical measure), provided that suitable martingale constraints are also imposed. Further, we introduce a relaxation of the martingale constraints which not only provides a unified viewpoint to a class of existing robust methods but also leads to new regularization tools. To realize these novel tools, tractable computational algorithms are proposed. As a byproduct, the strong duality theorem proved in this paper can be potentially applied to other problems of independent interest.
