Incorporating Unlabeled Data into Distributionally Robust Learning
This work improves DRL for machine learning practitioners by providing more reliable and confident classifiers with computable guarantees, though it is incremental as it builds on existing DRL frameworks.
The paper tackles the problem of distributionally robust learning (DRL) by addressing its overly broad adversary definitions, which lead to unconfident classifiers, by incorporating unlabeled data to constrain the adversary. The result is a tractable formulation that yields tighter performance guarantees and effective classifiers on 14 real datasets, often outperforming conventional DRL.
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.