# Stochastic Optimization for Performative Prediction

arXiv: https://arxiv.org/abs/2006.06887 · HTML: https://mlsanity.com/paper/2006.06887/

## Key facts

- Cited by 93 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2020.

## Built on by (most cited first, 30 of 93)

- [Online Decision Transformer](https://mlsanity.com/paper/2202.05607/) (2022)
- [Outside the Echo Chamber: Optimizing the Performative Risk](https://mlsanity.com/paper/2102.08570/) (2021)
- [How to Learn when Data Reacts to Your Model: Performative Gradient Descent](https://mlsanity.com/paper/2102.07698/) (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)
- [Alternative Microfoundations for Strategic Classification](https://mlsanity.com/paper/2106.12705/) (2021)
- [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)
- [Strategic Instrumental Variable Regression: Recovering Causal Relationships From Strategic Responses](https://mlsanity.com/paper/2107.05762/) (2021)
- [Decision-Dependent Risk Minimization in Geometrically Decaying Dynamic Environments](https://mlsanity.com/paper/2204.08281/) (2022)
- [How to Learn when Data Gradually Reacts to Your Model](https://mlsanity.com/paper/2112.07042/) (2021)
- [A Validity Perspective on Evaluating the Justified Use of Data-driven Decision-making Algorithms](https://mlsanity.com/paper/2206.14983/) (2022)
- [Performative Reinforcement Learning](https://mlsanity.com/paper/2207.00046/) (2022)
- [Plug-in Performative Optimization](https://mlsanity.com/paper/2305.18728/) (2023)
- [Zeroth-Order Methods for Convex-Concave Minmax Problems: Applications to Decision-Dependent Risk Minimization](https://mlsanity.com/paper/2106.09082/) (2021)
- [Stochastic Optimization under Distributional Drift](https://mlsanity.com/paper/2108.07356/) (2021)
- [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)
- [Human Expertise in Algorithmic Prediction](https://mlsanity.com/paper/2402.00793/) (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)
- [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)
- [Revisiting the Predictability of Performative, Social Events](https://mlsanity.com/paper/2503.11713/) (2025)

## Abstract (arXiv)

In performative prediction, the choice of a model influences the distribution of future data, typically through actions taken based on the model's predictions. We initiate the study of stochastic optimization for performative prediction. What sets this setting apart from traditional stochastic optimization is the difference between merely updating model parameters and deploying the new model. The latter triggers a shift in the distribution that affects future data, while the former keeps the distribution as is. Assuming smoothness and strong convexity, we prove rates of convergence for both greedily deploying models after each stochastic update (greedy deploy) as well as for taking several updates before redeploying (lazy deploy). In both cases, our bounds smoothly recover the optimal O(1/k) rate as the strength of performativity decreases. Furthermore, they illustrate how depending on the strength of performative effects, there exists a regime where either approach outperforms the other. We experimentally explore the trade-off on both synthetic data and a strategic classification simulator.