Title: Equalized Robustness: Towards Sustainable Fairness Under Distributional Shifts. Abstract: Increasing concerns have been raised on deep learning fairness in recent years. Existing fairness metrics and algorithms mainly focus on the discrimination of model performance across different groups on in-distribution data. It remains unclear whether the fairness achieved on in-distribution data can be generalized to data with unseen distribution shifts, which are commonly encountered in real-world applications. In this paper, we first propose a new fairness goal, termed Equalized Robustness (ER), to impose fair model robustness against unseen distribution shifts across majority and minority groups. ER measures robustness disparity by the maximum mean discrepancy (MMD) distance between the loss curvature distributions of two groups of data. We show that previous fairness learning algorithms designed for in-distribution fairness fail to meet the new robust fairness goal. We further propose a novel fairness learning algorithm, termed Curvature Matching (CUMA), to simultaneously achieve both traditional in-distribution fairness and our new robust fairness. CUMA efficiently debiases the model robustness by minimizing the MMD distance between loss curvature distributions of two groups. Experiments on three popular datasets show CUMA achieves superior fairness in robustness against distribution shifts, without more sacrifice on either overall accuracies or the in-distribution fairness.