Learning Models with Uniform Performance via Distributionally Robust Optimization

In many applications of statistics and machine learning, we wish to learn models that achieve uniformly good performance over almost all input values. This is important for safety-and fairnesscritical systems such as medical diagnosis, autonomous vehicles, criminal justice and credit evaluations, where poor performance on the tails of the inputs leads to high-cost system failures. Methods that optimize average performance, however, often produce models that suffer low performance on the "hard" instances of the population. For example, standard regressors obtained from maximum likelihood estimation can lose their predictive power on certain regions of covariates [57], so that high average performance comes at the expense of low performance on minority subpopulations. In this work, we propose and study a procedure that explicitly optimizes performance on tail inputs that suffer high loss. Modern datasets incorporate heterogeneous (but latent) subpopulations, and a natural goal is to perform well across all of these [57, 65, 21]. While many statistical models show strong average performance, their performance often deteriorates on minority groups underrepresented in the dataset. For example, speech recognition systems are inaccurate for people with minority accents [4]. In numerous other applications--such as facial recognition, automatic video captioning, language identification, academic recommender systems--performance varies significantly over different demographic groupings, such as race, gender, or age [38, 42, 18, 68, 76].