# Computing Strategic Responses to Non-Linear Classifiers

arXiv: https://arxiv.org/abs/2511.21560 · HTML: https://mlsanity.com/paper/2511.21560/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 16 references that are in the map.
- First posted on arXiv 26 Nov 2025.

## Builds on (most cited first, 8 of 8)

- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [The Social Cost of Strategic Classification](https://mlsanity.com/paper/1808.08460/) (2018)
- [How to Learn when Data Reacts to Your Model: Performative Gradient Descent](https://mlsanity.com/paper/2102.07698/) (2021)
- [PAC-Learning for Strategic Classification](https://mlsanity.com/paper/2012.03310/) (2020)
- [Generalized Strategic Classification and the Case of Aligned Incentives](https://mlsanity.com/paper/2202.04357/) (2022)
- [Performative Prediction with Neural Networks](https://mlsanity.com/paper/2304.06879/) (2023)
- [Nonlinear Performative Prediction](https://mlsanity.com/paper/2509.01139/) (2025)

## Abstract (arXiv)

We consider the problem of strategic classification, where the act of deploying a classifier leads to strategic behaviour that induces a distribution shift on subsequent observations. Current approaches to learning classifiers in strategic settings are focused primarily on the linear setting, but in many cases non-linear classifiers are more suitable. A central limitation to progress for non-linear classifiers arises from the inability to compute best responses in these settings. We present a novel method for computing the best response by optimising the Lagrangian dual of the Agents' objective. We demonstrate that our method reproduces best responses in linear settings, identifying key weaknesses in existing approaches. We present further results demonstrating our method can be straight-forwardly applied to non-linear classifier settings, where it is useful for both evaluation and training.