Adversarial training has proven to be a highly effective method for improving the robustness of deep neural networks against adversarial attacks. Nonetheless, it has been observed to exhibit a limitation in terms of robust fairness, characterized by a significant disparity in robustness across different classes. Recent efforts to mitigate this problem have turned to class-wise reweighted methods. However, these methods suffer from a lack of rigorous theoretical analysis and are limited in their exploration of the weight space, as they mainly rely on existing heuristic algorithms or intuition to compute weights. In addition, these methods fail to guarantee the consistency of the optimization direction due to the decoupled optimization of weights and the model parameters. They potentially lead to suboptimal weight assignments and consequently, a suboptimal model. To address these problems, this paper proposes a novel min-max training framework, Class Optimal Distribution Adversarial Training (CODAT), which employs distributionally robust optimization to fully explore the class-wise weight space, thus enabling the identification of the optimal weight with theoretical guarantees. Furthermore, we derive a closed-form optimal solution to the internal maximization and then get a deterministic equivalent objective function, which provides a theoretical basis for the joint optimization of weights and model parameters. Meanwhile, we propose a fairness elasticity coefficient for the evaluation of the algorithm with regard to both robustness and robust fairness. Experimental results on various datasets show that the proposed method can effectively improve the robust fairness of the model and outperform the state-of-the-art approaches.

Our mission is to make life easier for small and medium sized businesses, the backbone of our global economy. We do that by working with fintech companies and financial institutions to help them connect into the systems their small business customers use. With this connectivity, our clients are building next generation products to take the friction out of running a small business, from business management software to alternative lending and corporate cards. Codat is a Series C-funded company, backed by some of the leading investors and most successful tech companies in the world, including J.P. Morgan, Shopify, Plaid, PayPal Ventures, Amex Ventures, Index Ventures and Tiger Global. We have offices in London, New York and Sydney.

Our mission is to make life easier for small and medium sized businesses, the backbone of our global economy. We do that by working with fintech companies and financial institutions to help them connect into the systems their small business customers use. With this connectivity, our clients are building next generation products to take the friction out of running a small business, from business management software to alternative lending and corporate cards. Codat is a Series C-funded company, backed by some of the leading investors and most successful tech companies in the world, including J.P. Morgan, Shopify, Plaid, PayPal Ventures, Amex Ventures, Index Ventures and Tiger Global. We have offices in London, New York, Sydney.