# Tight Lower Bounds and Improved Convergence in Performative Prediction

arXiv: https://arxiv.org/abs/2412.03671 · HTML: https://mlsanity.com/paper/2412.03671/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 34 references that are in the map.
- First posted on arXiv 4 Dec 2024.

## Builds on (most cited first, 21 of 21)

- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Strategic Classification](https://mlsanity.com/paper/1506.06980/) (2015)
- [Recommendations as Treatments: Debiasing Learning and Evaluation](https://mlsanity.com/paper/1602.05352/) (2016)
- [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)
- [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)
- [Regret Minimization with Performative Feedback](https://mlsanity.com/paper/2202.00628/) (2022)
- [State Dependent Performative Prediction with Stochastic Approximation](https://mlsanity.com/paper/2110.00800/) (2021)
- [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)
- [Over-Optimization of Academic Publishing Metrics: Observing Goodhart's Law in Action](https://mlsanity.com/paper/1809.07841/) (2018)
- [Plug-in Performative Optimization](https://mlsanity.com/paper/2305.18728/) (2023)
- [Performative Reinforcement Learning in Gradually Shifting Environments](https://mlsanity.com/paper/2402.09838/) (2024)
- [Stochastic Optimization Schemes for Performative Prediction with Nonconvex Loss](https://mlsanity.com/paper/2405.17922/) (2024)
- [Approximate Regions of Attraction in Learning with Decision-Dependent Distributions](https://mlsanity.com/paper/2107.00055/) (2021)
- [Optimal Classification under Performative Distribution Shift](https://mlsanity.com/paper/2411.02023/) (2024)
- [Performative Prediction on Games and Mechanism Design](https://mlsanity.com/paper/2408.05146/) (2024)

## Built on by (most cited first, 4 of 4)

- [Revisiting the Predictability of Performative, Social Events](https://mlsanity.com/paper/2503.11713/) (2025)
- [Statistical Inference under Performativity](https://mlsanity.com/paper/2505.18493/) (2025)
- [On the Computational Complexity of Performative Prediction](https://mlsanity.com/paper/2601.20180/) (2026)
- [When Predictions Shape Reality: A Socio-Technical Synthesis of Performative Predictions in Machine Learning](https://mlsanity.com/paper/2601.04447/) (2026)

## Abstract (arXiv)

Performative prediction is a framework accounting for the shift in the data distribution induced by the prediction of a model deployed in the real world. Ensuring rapid convergence to a stable solution where the data distribution remains the same after the model deployment is crucial, especially in evolving environments. This paper extends the Repeated Risk Minimization (RRM) framework by utilizing historical datasets from previous retraining snapshots, yielding a class of algorithms that we call Affine Risk Minimizers and enabling convergence to a performatively stable point for a broader class of problems. We introduce a new upper bound for methods that use only the final iteration of the dataset and prove for the first time the tightness of both this new bound and the previous existing bounds within the same regime. We also prove that utilizing historical datasets can surpass the lower bound for last iterate RRM, and empirically observe faster convergence to the stable point on various performative prediction benchmarks. We offer at the same time the first lower bound analysis for RRM within the class of Affine Risk Minimizers, quantifying the potential improvements in convergence speed that could be achieved with other variants in our framework.