Providing users with alternatives to choose from is an essential component in many online platforms, making the accurate prediction of choice vital to their success. A renewed interest in learning choice models has led to significant progress in modeling power, but most current methods are either limited in the types of choice behavior they capture, cannot be applied to large-scale data, or both. Here we propose a learning framework for predicting choice that is accurate, versatile, theoretically grounded, and scales well. Our key modeling point is that to account for how humans choose, predictive models must capture certain set-related invariances. Building on recent results in economics, we derive a class of models that can express any behavioral choice pattern, enjoy favorable sample complexity guarantees, and can be efficiently trained end-to-end. Experiments on three large choice datasets demonstrate the utility of our approach.

Algorithms are increasingly common components of high-impact decision-making, and a growing body of literature on adversarial examples in laboratory settings indicates that standard machine learning models are not robust. This suggests that real-world systems are also susceptible to manipulation or misclassification, which especially poses a challenge to machine learning models used in financial services. We use the loan grade classification problem to explore how machine learning models are sensitive to small changes in user-reported data, using adversarial attacks documented in the literature and an original, domain-specific attack. Our work shows that a robust optimization algorithm can build models for financial services that are resistant to misclassification on perturbations. To the best of our knowledge, this is the first study of adversarial attacks and defenses for deep learning in financial services.