This paper addresses the problem of learning robust models under distributional shifts between training and test datasets. Existing invariant feature learning methods assume that invariant features are fully observed across both training and test sets, but in practice, this assumption is often violated. Therefore, models relying on invariant features absent from the test set may be less robust in new environments. To address this issue, this paper presents the Sufficient Invariant Learning (SIL) framework, a novel learning principle that learns a sufficient subset of invariant features instead of relying on a single feature. After demonstrating the limitations of existing invariant learning methods, we propose Adaptive Sharpness-Aware Group Distribution Robust Optimization (ASGDRO), a novel algorithm that learns diverse invariant features by finding common flat minima across environments. Theoretically, we demonstrate that finding common flat minima enables robust predictions based on diverse invariant features. Experimental evaluations on multiple datasets, including new benchmarks, confirm the robustness of ASGDRO to distributional shifts and highlight the limitations of existing methods.
