# How to Learn when Data Reacts to Your Model: Performative Gradient Descent

arXiv: https://arxiv.org/abs/2102.07698 · HTML: https://mlsanity.com/paper/2102.07698/

## Key facts

- Cited by 71 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 30 references that are in the map.
- First posted on arXiv 15 Feb 2021.

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

- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Strategic Classification](https://mlsanity.com/paper/1506.06980/) (2015)
- [Optimal rates for zero-order convex optimization: the power of two function evaluations](https://mlsanity.com/paper/1312.2139/) (2013)
- [Non-stationary Stochastic Optimization](https://mlsanity.com/paper/1307.5449/) (2013)
- [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)
- [How Do Classifiers Induce Agents To Invest Effort Strategically?](https://mlsanity.com/paper/1807.05307/) (2018)
- [On the Sentence Embeddings from Pre-trained Language Models](https://mlsanity.com/paper/2011.05864/) (2020)
- [Stochastic optimization with decision-dependent distributions](https://mlsanity.com/paper/2011.11173/) (2020)
- [Improved Regret for Zeroth-Order Adversarial Bandit Convex Optimisation](https://mlsanity.com/paper/2006.00475/) (2020)
- [Optimum Statistical Estimation with Strategic Data Sources](https://mlsanity.com/paper/1408.2539/) (2014)
- [Strategyproof Linear Regression in High Dimensions](https://mlsanity.com/paper/1805.10693/) (2018)
- [Optimal Decision Making Under Strategic Behavior](https://mlsanity.com/paper/1905.09239/) (2019)
- [Manipulation-Proof Machine Learning](https://mlsanity.com/paper/2004.03865/) (2020)
- [Gaming Helps! Learning from Strategic Interactions in Natural Dynamics](https://mlsanity.com/paper/2002.07024/) (2020)

## Built on by (most cited first, 30 of 71)

- [MetaShift: A Dataset of Datasets for Evaluating Contextual Distribution Shifts and Training Conflicts](https://mlsanity.com/paper/2202.06523/) (2022)
- [Data Feedback Loops: Model-driven Amplification of Dataset Biases](https://mlsanity.com/paper/2209.03942/) (2022)
- [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)
- [Performative Prediction: Past and Future](https://mlsanity.com/paper/2310.16608/) (2023)
- [Multiplayer Performative Prediction: Learning in Decision-Dependent Games](https://mlsanity.com/paper/2201.03398/) (2022)
- [Performative Power](https://mlsanity.com/paper/2203.17232/) (2022)
- [Regret Minimization with Performative Feedback](https://mlsanity.com/paper/2202.00628/) (2022)
- [Anticipating Performativity by Predicting from Predictions](https://mlsanity.com/paper/2208.07331/) (2022)
- [Performative Prediction with Neural Networks](https://mlsanity.com/paper/2304.06879/) (2023)
- [Multi-agent Performative Prediction: From Global Stability and Optimality to Chaos](https://mlsanity.com/paper/2201.10483/) (2022)
- [Making Decisions under Outcome Performativity](https://mlsanity.com/paper/2210.01745/) (2022)
- [How to Learn when Data Gradually Reacts to Your Model](https://mlsanity.com/paper/2112.07042/) (2021)
- [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)
- [Stochastic Approximation with Decision-Dependent Distributions: Asymptotic Normality and Optimality](https://mlsanity.com/paper/2207.04173/) (2022)
- [Performative Recommendation: Diversifying Content via Strategic Incentives](https://mlsanity.com/paper/2302.04336/) (2023)
- [Non-linear Welfare-Aware Strategic Learning](https://mlsanity.com/paper/2405.01810/) (2024)
- [Approximate Regions of Attraction in Learning with Decision-Dependent Distributions](https://mlsanity.com/paper/2107.00055/) (2021)
- [Performative Prediction with Bandit Feedback: Learning through Reparameterization](https://mlsanity.com/paper/2305.01094/) (2023)
- [Addressing Polarization and Unfairness in Performative Prediction](https://mlsanity.com/paper/2406.16756/) (2024)
- [Zero-Regret Performative Prediction Under Inequality Constraints](https://mlsanity.com/paper/2309.12618/) (2023)
- [Model Transferability With Responsive Decision Subjects](https://mlsanity.com/paper/2107.05911/) (2021)
- [Incentivizing honest performative predictions with proper scoring rules](https://mlsanity.com/paper/2305.17601/) (2023)
- [Automating Data Annotation under Strategic Human Agents: Risks and Potential Solutions](https://mlsanity.com/paper/2405.08027/) (2024)
- [Performative Reinforcement Learning with Linear Markov Decision Process](https://mlsanity.com/paper/2411.05234/) (2024)
- [Learning under Imitative Strategic Behavior with Unforeseeable Outcomes](https://mlsanity.com/paper/2405.01797/) (2024)
- [Performative Validity of Recourse Explanations](https://mlsanity.com/paper/2506.15366/) (2025)
- [Algorithmic Decision-Making under Agents with Persistent Improvement](https://mlsanity.com/paper/2405.01807/) (2024)

## Abstract (arXiv)

Performative distribution shift captures the setting where the choice of which ML model is deployed changes the data distribution. For example, a bank which uses the number of open credit lines to determine a customer's risk of default on a loan may induce customers to open more credit lines in order to improve their chances of being approved. Because of the interactions between the model and data distribution, finding the optimal model parameters is challenging. Works in this area have focused on finding stable points, which can be far from optimal. Here we introduce performative gradient descent (PerfGD), which is the first algorithm which provably converges to the performatively optimal point. PerfGD explicitly captures how changes in the model affects the data distribution and is simple to use. We support our findings with theory and experiments.