The objective of Domain Generalization (DG) is to devise algorithms and models capable of achieving high performance on previously unseen test distributions. In the pursuit of this objective, average measure has been employed as the prevalent measure for evaluating models and comparing algorithms in the existing DG studies. Despite its significance, a comprehensive exploration of the average measure has been lacking and its suitability in approximating the true domain generalization performance has been questionable. In this study, we carefully investigate the limitations inherent in the average measure and propose worst+gap measure as a robust alternative. We establish theoretical grounds of the proposed measure by deriving two theorems starting from two different assumptions. We conduct extensive experimental investigations to compare the proposed worst+gap measure with the conventional average measure. Given the indispensable need to access the true DG performance for studying measures, we modify five existing datasets to come up with SR-CMNIST, C-Cats&Dogs, L-CIFAR10, PACS-corrupted, and VLCS-corrupted datasets. The experiment results unveil an inferior performance of the average measure in approximating the true DG performance and confirm the robustness of the theoretically supported worst+gap measure.
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