Tilted Empirical Risk Minimization
This work tackles the problem of improving machine learning model robustness, fairness, and generalization for practitioners by offering a flexible, unified alternative to specialized solutions.
The paper introduces Tilted Empirical Risk Minimization (TERM), a unified framework that extends ERM with a tilt hyperparameter to flexibly tune individual loss impacts, addressing problems like outlier sensitivity, poor generalization, and unfairness. It shows TERM is competitive with specialized methods for applications such as fairness, robustness, and class imbalance, and enables new uses like combining outlier mitigation with fairness.
Empirical risk minimization (ERM) is typically designed to perform well on the average loss, which can result in estimators that are sensitive to outliers, generalize poorly, or treat subgroups unfairly. While many methods aim to address these problems individually, in this work, we explore them through a unified framework -- tilted empirical risk minimization (TERM). In particular, we show that it is possible to flexibly tune the impact of individual losses through a straightforward extension to ERM using a hyperparameter called the tilt. We provide several interpretations of the resulting framework: We show that TERM can increase or decrease the influence of outliers, respectively, to enable fairness or robustness; has variance-reduction properties that can benefit generalization; and can be viewed as a smooth approximation to a superquantile method. We develop batch and stochastic first-order optimization methods for solving TERM, and show that the problem can be efficiently solved relative to common alternatives. Finally, we demonstrate that TERM can be used for a multitude of applications, such as enforcing fairness between subgroups, mitigating the effect of outliers, and handling class imbalance. TERM is not only competitive with existing solutions tailored to these individual problems, but can also enable entirely new applications, such as simultaneously addressing outliers and promoting fairness.