Data-driven Optimal Transport Cost Selection for Distributionally Robust Optimizatio

05/19/2017
by   Jose Blanchet, et al.
0

Recently, (Blanchet, Kang, and Murhy 2016) 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 is defined as a neighborhood centered at the empirical distribution. 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.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset