Online Combinatorial Optimization with Group Fairness Constraints

As digital marketplaces and services continue to expand, it is crucial to maintain a safe and fair environment for all users. This requires implementing fairness constraints into the sequential decision-making processes of these platforms to ensure equal treatment. However, this can be challenging as these processes often need to solve NP-complete problems with exponentially large decision spaces at each time step. To overcome this, we propose a general framework incorporating robustness and fairness into NP-complete problems, such as optimizing product ranking and maximizing sub-modular functions. Our framework casts the problem as a max-min game between a primal player aiming to maximize the platform's objective and a dual player in charge of group fairness constraints. We show that one can trace the entire Pareto fairness curve by changing the thresholds on the fairness constraints. We provide theoretical guarantees for our method and empirically evaluate it, demonstrating its effectiveness.