# Emergent specialization from participation dynamics and multi-learner retraining

arXiv: https://arxiv.org/abs/2206.02667 · HTML: https://mlsanity.com/paper/2206.02667/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 48 references that are in the map.
- First posted on arXiv 6 Jun 2022.

## Builds on (most cited first, 22 of 22)

- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Fairness Without Demographics in Repeated Loss Minimization](https://mlsanity.com/paper/1806.08010/) (2018)
- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Strategic Classification](https://mlsanity.com/paper/1506.06980/) (2015)
- [Outside the Echo Chamber: Optimizing the Performative Risk](https://mlsanity.com/paper/2102.08570/) (2021)
- [Stochastic Optimization for Performative Prediction](https://mlsanity.com/paper/2006.06887/) (2020)
- [Performative Prediction in a Stateful World](https://mlsanity.com/paper/2011.03885/) (2020)
- [Guarantees for Spectral Clustering with Fairness Constraints](https://mlsanity.com/paper/1901.08668/) (2019)
- [How to Learn when Data Reacts to Your Model: Performative Gradient Descent](https://mlsanity.com/paper/2102.07698/) (2021)
- [Fair k-Center Clustering for Data Summarization](https://mlsanity.com/paper/1901.08628/) (2019)
- [Stochastic optimization with decision-dependent distributions](https://mlsanity.com/paper/2011.11173/) (2020)
- [Multiplayer Performative Prediction: Learning in Decision-Dependent Games](https://mlsanity.com/paper/2201.03398/) (2022)
- [Performative Power](https://mlsanity.com/paper/2203.17232/) (2022)
- [Group Retention when Using Machine Learning in Sequential Decision Making: the Interplay between User Dynamics and Fairness](https://mlsanity.com/paper/1905.00569/) (2019)
- [On Almost Sure Convergence Rates of Stochastic Gradient Methods](https://mlsanity.com/paper/2202.04295/) (2022)
- [Multi-agent Performative Prediction: From Global Stability and Optimality to Chaos](https://mlsanity.com/paper/2201.10483/) (2022)
- [Decision-Dependent Risk Minimization in Geometrically Decaying Dynamic Environments](https://mlsanity.com/paper/2204.08281/) (2022)
- [Online Projected Gradient Descent for Stochastic Optimization with Decision-Dependent Distributions](https://mlsanity.com/paper/2107.09721/) (2021)
- [Lyapunov Theory for Discrete Time Systems](https://mlsanity.com/paper/1809.05289/) (2018)
- [Regression Equilibrium](https://mlsanity.com/paper/1905.02576/) (2019)
- [Competing Bandits: The Perils of Exploration Under Competition](https://mlsanity.com/paper/2007.10144/) (2020)
- [Stochastic Saddle Point Problems with Decision-Dependent Distributions](https://mlsanity.com/paper/2201.02313/) (2022)

## Built on by (most cited first, 5 of 5)

- [Algorithmic Decision-Making under Agents with Persistent Improvement](https://mlsanity.com/paper/2405.01807/) (2024)
- [A Market for Accuracy: Classification under Competition](https://mlsanity.com/paper/2502.18052/) (2025)
- [Safety vs. Performance: How Multi-Objective Learning Reduces Barriers to Market Entry](https://mlsanity.com/paper/2409.03734/) (2024)
- [Learning from Streaming Data when Users Choose](https://mlsanity.com/paper/2406.01481/) (2024)
- [Evolutionary Prediction Games](https://mlsanity.com/paper/2503.03401/) (2025)

## Abstract (arXiv)

Numerous online services are data-driven: the behavior of users affects the system's parameters, and the system's parameters affect the users' experience of the service, which in turn affects the way users may interact with the system. For example, people may choose to use a service only for tasks that already works well, or they may choose to switch to a different service. These adaptations influence the ability of a system to learn about a population of users and tasks in order to improve its performance broadly. In this work, we analyze a class of such dynamics -- where users allocate their participation amongst services to reduce the individual risk they experience, and services update their model parameters to reduce the service's risk on their current user population. We refer to these dynamics as risk-reducing, which cover a broad class of common model updates including gradient descent and multiplicative weights. For this general class of dynamics, we show that asymptotically stable equilibria are always segmented, with sub-populations allocated to a single learner. Under mild assumptions, the utilitarian social optimum is a stable equilibrium. In contrast to previous work, which shows that repeated risk minimization can result in (Hashimoto et al., 2018; Miller et al., 2021), we find that repeated myopic updates with multiple learners lead to better outcomes. We illustrate the phenomena via a simulated example initialized from real data.