# Nonlinear Performative Prediction

arXiv: https://arxiv.org/abs/2509.01139 · HTML: https://mlsanity.com/paper/2509.01139/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 40 references that are in the map.
- First posted on arXiv 1 Sep 2025.

## Builds on (most cited first, 19 of 19)

- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [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)
- [Multiplayer Performative Prediction: Learning in Decision-Dependent Games](https://mlsanity.com/paper/2201.03398/) (2022)
- [Performative Power](https://mlsanity.com/paper/2203.17232/) (2022)
- [State Dependent Performative Prediction with Stochastic Approximation](https://mlsanity.com/paper/2110.00800/) (2021)
- [Performative Prediction with Neural Networks](https://mlsanity.com/paper/2304.06879/) (2023)
- [How to Learn when Data Gradually Reacts to Your Model](https://mlsanity.com/paper/2112.07042/) (2021)
- [Performative Reinforcement Learning](https://mlsanity.com/paper/2207.00046/) (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 Recommendation: Diversifying Content via Strategic Incentives](https://mlsanity.com/paper/2302.04336/) (2023)
- [Performative Prediction with Bandit Feedback: Learning through Reparameterization](https://mlsanity.com/paper/2305.01094/) (2023)
- [Zero-Regret Performative Prediction Under Inequality Constraints](https://mlsanity.com/paper/2309.12618/) (2023)
- [Two-timescale Derivative Free Optimization for Performative Prediction with Markovian Data](https://mlsanity.com/paper/2310.05792/) (2023)
- [Performative Debias with Fair-exposure Optimization Driven by Strategic Agents in Recommender Systems](https://mlsanity.com/paper/2406.17475/) (2024)

## Built on by (most cited first, 2 of 2)

- [Computing Strategic Responses to Non-Linear Classifiers](https://mlsanity.com/paper/2511.21560/) (2025)
- [Non-Linear Strategic Classification Made Practical](https://mlsanity.com/paper/2606.28204/) (2026)

## Abstract (arXiv)

Performative prediction is an emerging paradigm in machine learning that addresses scenarios where the model's prediction may induce a shift in the distribution of the data it aims to predict. Current works in this field often rely on uncontrollable assumptions, such as bounded gradients of performative loss, and primarily focus on linear cases in their examples and evaluations to maintain consistency between theoretical guarantees and empirical validations. However, such linearity rarely holds in real-world applications, where the data usually exhibit complex nonlinear characteristics. In this paper, we relax these out-of-control assumptions and present a novel design that generalizes performative prediction to nonlinear cases while preserving essential theoretical properties. Specifically, we formulate the loss function of performative prediction using a maximum margin approach and extend it to nonlinear spaces through kernel methods. To quantify the data distribution shift, we employ the discrepancy between prediction errors on these two distributions as an indicator, which characterizes the impact of the performative effect on specific learning tasks. By doing so, we can derive, for both linear and nonlinear cases, the conditions for performative stability, a critical and desirable property in performative contexts. Building on these theoretical insights, we develop an algorithm that guarantees the performative stability of the predictive model. We validate the effectiveness of our method through experiments on synthetic and real-world datasets with both linear and nonlinear data distributions, demonstrating superior performance compared to state-of-the-art baselines.