Abstract: Learning invariant representations is a fundamental requirement for training machine learning models that are influenced by spurious correlations. These spurious correlations, present in the training datasets, wrongly direct the neural network predictions resulting in reduced performance on certain groups, especially the minority groups. Robust training against such correlations requires the knowledge of group membership on every training sample. This need is impractical in situations where the data labeling efforts, for minority/rare groups, are significantly laborious or where the individuals comprising the dataset choose to conceal sensitive information pertaining to the groups. On the other hand, the presence of data collection efforts often results in datasets that contain partially labeled group information. Recent works, addressing the problem, have tackled fully unsupervised scenarios where no labels for groups are available. We aim to fill a missing gap in the literature that addresses a more realistic setting by leveraging partially available group information during training. First, we construct a constraint set and derive a high probability bound for the group assignment to belong to the set. Second, we propose an algorithm that optimizes for a worst-off group assignment from the constraint set. Through experiments on image and tabular datasets, we show improvements in the minority group's performance while preserving overall accuracy across groups.