# Asymptotically Fair Participation in Machine Learning Models: an Optimal Control Perspective

arXiv: https://arxiv.org/abs/2311.10223 · HTML: https://mlsanity.com/paper/2311.10223/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 38 references that are in the map.
- First posted on arXiv 16 Nov 2023.

## Builds on (most cited first, 18 of 18)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Certifying and removing disparate impact](https://mlsanity.com/paper/1412.3756/) (2014)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [Fairness Without Demographics in Repeated Loss Minimization](https://mlsanity.com/paper/1806.08010/) (2018)
- [Stable Architectures for Deep Neural Networks](https://mlsanity.com/paper/1705.03341/) (2017)
- [Delayed Impact of Fair Machine Learning](https://mlsanity.com/paper/1803.04383/) (2018)
- [Maximum Principle Based Algorithms for Deep Learning](https://mlsanity.com/paper/1710.09513/) (2017)
- [A Mean-Field Optimal Control Formulation of Deep Learning](https://mlsanity.com/paper/1807.01083/) (2018)
- [How Do Fair Decisions Fare in Long-term Qualification?](https://mlsanity.com/paper/2010.11300/) (2020)
- [Group Retention when Using Machine Learning in Sequential Decision Making: the Interplay between User Dynamics and Fairness](https://mlsanity.com/paper/1905.00569/) (2019)
- [Deep Learning Theory Review: An Optimal Control and Dynamical Systems Perspective](https://mlsanity.com/paper/1908.10920/) (2019)
- [An Optimal Control Approach to Deep Learning and Applications to Discrete-Weight Neural Networks](https://mlsanity.com/paper/1803.01299/) (2018)
- [ProPublica's COMPAS Data Revisited](https://mlsanity.com/paper/1906.04711/) (2019)
- [Towards Robust Neural Networks via Close-loop Control](https://mlsanity.com/paper/2102.01862/) (2021)
- [Self-Healing Robust Neural Networks via Closed-Loop Control](https://mlsanity.com/paper/2206.12963/) (2022)
- [DDPNOpt: Differential Dynamic Programming Neural Optimizer](https://mlsanity.com/paper/2002.08809/) (2020)

## Built on by (most cited first, 1 of 1)

- [PID Control-Based Self-Healing to Improve the Robustness of Large Language Models](https://mlsanity.com/paper/2404.00828/) (2024)

## Abstract (arXiv)

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.