# How to Learn when Data Gradually Reacts to Your Model

arXiv: https://arxiv.org/abs/2112.07042 · HTML: https://mlsanity.com/paper/2112.07042/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 29 references that are in the map.
- First posted on arXiv 13 Dec 2021.

## Builds on (most cited first, 16 of 16)

- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [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)
- [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)
- [How to Learn when Data Reacts to Your Model: Performative Gradient Descent](https://mlsanity.com/paper/2102.07698/) (2021)
- [Strategic Classification in the Dark](https://mlsanity.com/paper/2102.11592/) (2021)
- [Stochastic optimization with decision-dependent distributions](https://mlsanity.com/paper/2011.11173/) (2020)
- [Strategic Classification Made Practical](https://mlsanity.com/paper/2103.01826/) (2021)
- [Who Leads and Who Follows in Strategic Classification?](https://mlsanity.com/paper/2106.12529/) (2021)
- [PAC-Learning for Strategic Classification](https://mlsanity.com/paper/2012.03310/) (2020)
- [Alternative Microfoundations for Strategic Classification](https://mlsanity.com/paper/2106.12705/) (2021)
- [State Dependent Performative Prediction with Stochastic Approximation](https://mlsanity.com/paper/2110.00800/) (2021)
- [Visualization Equilibrium](https://mlsanity.com/paper/2108.04953/) (2021)

## Built on by (most cited first, 30 of 30)

- [MetaShift: A Dataset of Datasets for Evaluating Contextual Distribution Shifts and Training Conflicts](https://mlsanity.com/paper/2202.06523/) (2022)
- [Performative Prediction: Past and Future](https://mlsanity.com/paper/2310.16608/) (2023)
- [Making Decisions under Outcome Performativity](https://mlsanity.com/paper/2210.01745/) (2022)
- [Plug-in Performative Optimization](https://mlsanity.com/paper/2305.18728/) (2023)
- [Performative Federated Learning: A Solution to Model-Dependent and Heterogeneous Distribution Shifts](https://mlsanity.com/paper/2305.05090/) (2023)
- [Performative Reinforcement Learning in Gradually Shifting Environments](https://mlsanity.com/paper/2402.09838/) (2024)
- [Optimal Classification under Performative Distribution Shift](https://mlsanity.com/paper/2411.02023/) (2024)
- [Performative Reinforcement Learning with Linear Markov Decision Process](https://mlsanity.com/paper/2411.05234/) (2024)
- [Distributionally Robust Performative Prediction](https://mlsanity.com/paper/2412.04346/) (2024)
- [Data-Driven Subgroup Identification for Linear Regression](https://mlsanity.com/paper/2305.00195/) (2023)
- [Learning In Reverse Causal Strategic Environments With Ramifications on Two Sided Markets](https://mlsanity.com/paper/2404.13240/) (2024)
- [Performative Policy Gradient: Optimality in Performative Reinforcement Learning](https://mlsanity.com/paper/2512.20576/) (2025)
- [Independent Learning in Performative Markov Potential Games](https://mlsanity.com/paper/2504.20593/) (2025)
- [On the Impact of Performative Risk Minimization for Binary Random Variables](https://mlsanity.com/paper/2502.02331/) (2025)
- [Parameter-Free Algorithms for Performative Regret Minimization under Decision-Dependent Distributions](https://mlsanity.com/paper/2402.15188/) (2024)
- [Microfoundation Inference for Strategic Prediction](https://mlsanity.com/paper/2411.08998/) (2024)
- [Nonlinear Performative Prediction](https://mlsanity.com/paper/2509.01139/) (2025)
- [Dissecting Performative Prediction: A Comprehensive Survey](https://mlsanity.com/paper/2602.10176/) (2026)
- [Partially Performative Prediction](https://mlsanity.com/paper/2606.07890/) (2026)
- [Performative Drift Resistant Classification Using Generative Domain Adversarial Networks](https://mlsanity.com/paper/2504.01135/) (2025)
- [Optimal Regularization for Performative Learning](https://mlsanity.com/paper/2510.12249/) (2025)
- [Retraining Seeks Stable Signals](https://mlsanity.com/paper/2607.15623/) (2026)
- [The Role of Causality in Algorithmic Recourse](https://mlsanity.com/paper/2607.28497/) (2026)
- [Towards Performatively Stable Equilibria in Decision-Dependent Games for Arbitrary Data Distribution Maps](https://mlsanity.com/paper/2509.02619/) (2025)
- [When Predictions Shape Reality: A Socio-Technical Synthesis of Performative Predictions in Machine Learning](https://mlsanity.com/paper/2601.04447/) (2026)
- [Distributed Learning with Adversarial Gradient Perturbations](https://mlsanity.com/paper/2605.03313/) (2026)
- [Adaptive Gradient-Based Methods for a Broader Class of Optimization Problems under Performative Prediction](https://mlsanity.com/paper/2607.26562/) (2026)
- [Local and Global Stability in Performative Reinforcement Learning](https://mlsanity.com/paper/2609.06467/) (2026)
- [Algorithmic Recourse Under Competition](https://mlsanity.com/paper/2609.39877/) (2026)
- [Partially Informed Stochastic Optimization via Zeroth-Order Residual Tracking](https://mlsanity.com/paper/2610.13871/) (2026)

## Abstract (arXiv)

A recent line of work has focused on training machine learning (ML) models in the performative setting, i.e. when the data distribution reacts to the deployed model. The goal in this setting is to learn a model which both induces a favorable data distribution and performs well on the induced distribution, thereby minimizing the test loss. Previous work on finding an optimal model assumes that the data distribution immediately adapts to the deployed model. In practice, however, this may not be the case, as the population may take time to adapt to the model. In many applications, the data distribution depends on both the currently deployed ML model and on the "state" that the population was in before the model was deployed. In this work, we propose a new algorithm, Stateful Performative Gradient Descent (Stateful PerfGD), for minimizing the performative loss even in the presence of these effects. We provide theoretical guarantees for the convergence of Stateful PerfGD. Our experiments confirm that Stateful PerfGD substantially outperforms previous state-of-the-art methods.