The performance of state-of-the-art machine learning models is observed to degrade in scenarios involving under-represented demographic populations during training.This issue has been extensively studied within a supervised learning framework where data distribution remains unchanged.Nonetheless, real-world use cases often encounter distribution shifts induced by the models in deployment. For example, performance bias against minority users can affect customer retention rates, thereby skewing available data from active users due to the absence of minority user input.This feedback effect further exacerbates the discrepancy across various demographic groups in subsequent time steps. To mitigate this problem, we introduce asymptotic fairness, a criterion that aims at preserving sustained model performance across all demographic populations.In addition, we construct a surrogate retention system, based on existing literature on evolutionary population dynamics, to approximate the dynamics of distribution shifts on active user counts. This system allows the aim of achieving asymptotic fairness to be formulated as an optimal control problem.To evaluate the effectiveness of the proposed method,we design a generic simulation environment that simulates the population dynamics of the feedback effect between user retention and model performance.When we deploy the models to this simulation environment,by considering long-term planning,the optimal control solution outperforms existing baseline methods, demonstrating superior performance.