We study a robust alternative to empirical risk minimization called distributionally robust learning (DRL), in which one learns to perform against an adversary who can choose the data distribution from a specified set of distributions. We illustrate a problem with current DRL formulations, which rely on an overly broad definition of allowed distributions for the adversary, leading to learned classifiers that are unable to predict with any confidence. We propose a solution that incorporates unlabeled data into the DRL problem to further constrain the adversary. We show that this new formulation is tractable for stochastic gradient-based optimization and yields a computable guarantee on the future performance of the learned classifier, analogous to -- but tighter than -- guarantees from conventional DRL. We examine the performance of this new formulation on 14 real datasets and find that it often yields effective classifiers with nontrivial performance guarantees in situations where conventional DRL produces neither. Inspired by these results, we extend our DRL formulation to active learning with a novel, distributionally-robust version of the standard model-change heuristic. Our active learning algorithm often achieves superior learning performance to the original heuristic on real datasets.

本研究介绍了一种新的分布鲁棒学习方法，该方法通过加入无标签数据以限制敌手从指定分布中选择数据，可以有效地进行分类，并提出了一个分布鲁棒的版本，可应用于主动学习。在14个真实数据集上的结果表明，该算法往往在传统方法无法提供良好结果的情况下表现出色。

将未标记数据纳入分布鲁棒学习中