Counterfactual fairness alleviates the discrimination between the model prediction toward an individual in the actual world (observational data) and that in counterfactual world (i.e., what if the individual belongs to other sensitive groups). The existing studies need to pre-define the structural causal model that captures the correlations among variables for counterfactual inference; however, the underlying causal model is usually unknown and difficult to be validated in real-world scenarios. Moreover, the misspecification of the causal model potentially leads to poor performance in model prediction and thus makes unfair decisions. In this research, we propose a novel minimax game-theoretic model for counterfactual fairness that can produce accurate results meanwhile achieve a counterfactually fair decision with the relaxation of strong assumptions of structural causal models. In addition, we also theoretically prove the error bound of the proposed minimax model. Empirical experiments on multiple real-world datasets illustrate our superior performance in both accuracy and fairness. Source code is available at \url{https://github.com/tridungduong16/counterfactual_fairness_game_theoretic}.

翻译：反事实公平旨在缓解模型对实际世界（观测数据）中个体预测与反事实世界（即该个体若属于其他敏感群体时）中的预测之间的歧视。现有研究需预先定义结构因果模型以捕捉变量间的相关性，从而进行反事实推理；然而，在现实场景中，潜在的因果模型通常未知且难以验证。此外，因果模型的错误设定可能导致模型预测性能低下，进而做出不公平的决策。在本研究中，我们提出了一种新颖的极小极大博弈论模型来实现反事实公平，该模型在放松结构因果模型强假设的条件下，既能生成准确结果，又能做出反事实公平的决策。此外，我们从理论上证明了所提极小极大模型的误差界。在多个真实数据集上的实证实验表明，我们在准确性和公平性方面均具有优越性能。源代码见 \url{https://github.com/tridungduong16/counterfactual_fairness_game_theoretic}。