Data-driven Optimal Cost Selection for Distributionally Robust Optimization
This work addresses the challenge of parameter tuning in DRO for machine learning practitioners, offering an incremental improvement over existing methods.
The authors tackled the problem of selecting the uncertainty neighborhood size in distributionally robust optimization (DRO) by proposing a data-driven methodology that learns this parameter, showing it can improve upon various popular machine learning estimators in empirical demonstrations.
Recently, (Blanchet, Kang, and Murhy 2016, and Blanchet, and Kang 2017) 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.