# Approximate Regions of Attraction in Learning with Decision-Dependent Distributions

arXiv: https://arxiv.org/abs/2107.00055 · HTML: https://mlsanity.com/paper/2107.00055/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 26 references that are in the map.
- First posted on arXiv 30 Jun 2021.

## Builds on (most cited first, 12 of 12)

- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Strategic Classification](https://mlsanity.com/paper/1506.06980/) (2015)
- [Strategic Classification from Revealed Preferences](https://mlsanity.com/paper/1710.07887/) (2017)
- [The Social Cost of Strategic Classification](https://mlsanity.com/paper/1808.08460/) (2018)
- [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)
- [Strategic Classification is Causal Modeling in Disguise](https://mlsanity.com/paper/1910.10362/) (2019)
- [Performative Prediction in a Stateful World](https://mlsanity.com/paper/2011.03885/) (2020)
- [The Disparate Effects of Strategic Manipulation](https://mlsanity.com/paper/1808.08646/) (2018)
- [How to Learn when Data Reacts to Your Model: Performative Gradient Descent](https://mlsanity.com/paper/2102.07698/) (2021)
- [Stochastic optimization with decision-dependent distributions](https://mlsanity.com/paper/2011.11173/) (2020)
- [Price of Transparency in Strategic Machine Learning](https://mlsanity.com/paper/1610.08210/) (2016)

## Built on by (most cited first, 11 of 11)

- [Performative Power](https://mlsanity.com/paper/2203.17232/) (2022)
- [Regret Minimization with Performative Feedback](https://mlsanity.com/paper/2202.00628/) (2022)
- [Performative Prediction with Neural Networks](https://mlsanity.com/paper/2304.06879/) (2023)
- [Performative Prediction with Bandit Feedback: Learning through Reparameterization](https://mlsanity.com/paper/2305.01094/) (2023)
- [Distributionally Robust Performative Prediction](https://mlsanity.com/paper/2412.04346/) (2024)
- [Tight Lower Bounds and Improved Convergence in Performative Prediction](https://mlsanity.com/paper/2412.03671/) (2024)
- [Long Term Fairness for Minority Groups via Performative Distributionally Robust Optimization](https://mlsanity.com/paper/2207.05777/) (2022)
- [Parameter-Free Algorithms for Performative Regret Minimization under Decision-Dependent Distributions](https://mlsanity.com/paper/2402.15188/) (2024)
- [Dissecting Performative Prediction: A Comprehensive Survey](https://mlsanity.com/paper/2602.10176/) (2026)
- [On the Stochastic (Variance-Reduced) Proximal Gradient Method for Regularized Expected Reward Optimization](https://mlsanity.com/paper/2401.12508/) (2024)
- [When Predictions Shape Reality: A Socio-Technical Synthesis of Performative Predictions in Machine Learning](https://mlsanity.com/paper/2601.04447/) (2026)

## Abstract (arXiv)

As data-driven methods are deployed in real-world settings, the processes that generate the observed data will often react to the decisions of the learner. For example, a data source may have some incentive for the algorithm to provide a particular label (e.g. approve a bank loan), and manipulate their features accordingly. Work in strategic classification and decision-dependent distributions seeks to characterize the closed-loop behavior of deploying learning algorithms by explicitly considering the effect of the classifier on the underlying data distribution. More recently, works in performative prediction seek to classify the closed-loop behavior by considering general properties of the mapping from classifier to data distribution, rather than an explicit form. Building on this notion, we analyze repeated risk minimization as the perturbed trajectories of the gradient flows of performative risk minimization. We consider the case where there may be multiple local minimizers of performative risk, motivated by situations where the initial conditions may have significant impact on the long-term behavior of the system. We provide sufficient conditions to characterize the region of attraction for the various equilibria in this settings. Additionally, we introduce the notion of performative alignment, which provides a geometric condition on the convergence of repeated risk minimization to performative risk minimizers.