# Outside the Echo Chamber: Optimizing the Performative Risk

arXiv: https://arxiv.org/abs/2102.08570 · HTML: https://mlsanity.com/paper/2102.08570/

## Key facts

- Cited by 96 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 52 references that are in the map.
- First posted on arXiv 17 Feb 2021.

## Builds on (most cited first, 20 of 20)

- [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)
- [Model-Based Reinforcement Learning with a Generative Model is Minimax Optimal](https://mlsanity.com/paper/1906.03804/) (2019)
- [Naive Exploration is Optimal for Online LQR](https://mlsanity.com/paper/2001.09576/) (2020)
- [The Social Cost of Strategic Classification](https://mlsanity.com/paper/1808.08460/) (2018)
- [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)
- [Double/Debiased/Neyman Machine Learning of Treatment Effects](https://mlsanity.com/paper/1701.08687/) (2017)
- [The Disparate Effects of Strategic Manipulation](https://mlsanity.com/paper/1808.08646/) (2018)
- [Causal Strategic Linear Regression](https://mlsanity.com/paper/2002.10066/) (2020)
- [Stochastic optimization with decision-dependent distributions](https://mlsanity.com/paper/2011.11173/) (2020)
- [Maximizing Welfare with Incentive-Aware Evaluation Mechanisms](https://mlsanity.com/paper/2011.01956/) (2020)
- [Decisions, Counterfactual Explanations and Strategic Behavior](https://mlsanity.com/paper/2002.04333/) (2020)
- [Orthogonal Machine Learning: Power and Limitations](https://mlsanity.com/paper/1711.00342/) (2017)
- [A Tutorial on Concentration Bounds for System Identification](https://mlsanity.com/paper/1906.11395/) (2019)
- [From Predictions to Decisions: Using Lookahead Regularization](https://mlsanity.com/paper/2006.11638/) (2020)
- [Experimenting in Equilibrium](https://mlsanity.com/paper/1903.02124/) (2019)
- [Gaming Helps! Learning from Strategic Interactions in Natural Dynamics](https://mlsanity.com/paper/2002.07024/) (2020)

## Built on by (most cited first, 30 of 96)

- [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)
- [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)
- [Causal Strategic Classification: A Tale of Two Shifts](https://mlsanity.com/paper/2302.06280/) (2023)
- [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)
- [Strategic Classification with Graph Neural Networks](https://mlsanity.com/paper/2205.15765/) (2022)
- [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)
- [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)
- [Zero-Regret Performative Prediction Under Inequality Constraints](https://mlsanity.com/paper/2309.12618/) (2023)
- [Optimal Classification under Performative Distribution Shift](https://mlsanity.com/paper/2411.02023/) (2024)

## Abstract (arXiv)

In performative prediction, predictions guide decision-making and hence can influence the distribution of future data. To date, work on performative prediction has focused on finding performatively stable models, which are the fixed points of repeated retraining. However, stable solutions can be far from optimal when evaluated in terms of the performative risk, the loss experienced by the decision maker when deploying a model. In this paper, we shift attention beyond performative stability and focus on optimizing the performative risk directly. We identify a natural set of properties of the loss function and model-induced distribution shift under which the performative risk is convex, a property which does not follow from convexity of the loss alone. Furthermore, we develop algorithms that leverage our structural assumptions to optimize the performative risk with better sample efficiency than generic methods for derivative-free convex optimization.