Asymptotically Fair Participation in Machine Learning Models: an Optimal
  Control Perspective
Zhuotong Chen Qianxiao Li Zheng Zhang
The performance of state-of-the-art machine learning models often
deteriorates when testing on demographics that are under-represented in the
training dataset. This problem has predominately been studied in a supervised
learning setting where the data distribution is static. However, real-world
applications often involve distribution shifts caused by the deployed models.
For instance, the performance disparity against monitory users can lead to a
high customer churn rate, thus the available data provided by active users are
skewed due to the lack of minority users. This feedback effect further
exacerbates the disparity among different demographic groups in future steps.
To address this issue, we propose asymptotically fair participation as a
condition to maintain long-term model performance over all demographic groups.
In this work, we aim to address the problem of achieving asymptotically fair
participation via optimal control formulation. Moreover, we design a surrogate
retention system based on existing literature on evolutionary population
dynamics to approximate the dynamics of distribution shifts on active user
counts, from which the objective of achieving asymptotically fair participation
is formulated as an optimal control problem, and the control variables are
considered as the model parameters. We apply an efficient implementation of
Pontryagin's maximum principle to estimate the optimal control solution. 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
resulting models to the simulation environment, the optimal control solution
accounts for long-term planning and leads to superior performance compared with
existing baseline methods.