When is invariance useful in an Out-of-Distribution Generalization problem ?

Understand

The goal of Out-of-Distribution (OOD) generalization problem is to train a predictor that generalizes on all environments.

• Popular approaches in this field use the hypothesis that such a predictor shall be an \textit{invariant predictor} that captures the mechanism that remains constant across environments.
• While these approaches have been experimentally successful in various case studies, there is still much room for the theoretical validation of this hypothesis.
• This paper presents a new set of theoretical conditions necessary for an invariant predictor to achieve the OOD optimality.