Tilted Empirical Risk Minimization

Understand

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.