An Online Learning Approach to Interpolation and Extrapolation in Domain Generalization

Modern machine learning algorithms excel when the training and test distributions match but often fail under even moderate distribution shift (Beery et al., 2018); learning a predictor which generalizes to distributions which differ from the training data is therefore an important task. This objective, broadly referred to as out-of-distribution (OOD) generalization, is not realizable in general, so researchers have formalized several possible restrictions. Common choices include a structural assumption such as covariate or label shift (Widmer & Kubat, 1996; Bickel et al., 2009; Lipton et al., 2018) or expecting that the test distribution will lie in some uncertainty set around the training distribution (Bagnell, 2005; Rahimian & Mehrotra, 2019). One popular assumption is that the training data is comprised of a collection of "environments" (Blanchard et al., 2011; Muandet et al., 2013; Peters et al., 2016) or "groups" (Sagawa et al., 2020), each representing a distinct distribution, where the group identity of each sample is known. The hope is that by cleverly training on such a combination of groups, one can derive a robust predictor which will better transfer to unseen test data which relates to the observed distributions--such a task is known as domain generalization.