# Non-Linear Strategic Classification Made Practical

arXiv: https://arxiv.org/abs/2606.28204 · HTML: https://mlsanity.com/paper/2606.28204/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 36 references that are in the map.
- First posted on arXiv 26 Jun 2026.

## Builds on (most cited first, 26 of 26)

- [Meta-Learning with Implicit Gradients](https://mlsanity.com/paper/1909.04630/) (2019)
- [Bilevel Programming for Hyperparameter Optimization and Meta-Learning](https://mlsanity.com/paper/1806.04910/) (2018)
- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Optimizing Millions of Hyperparameters by Implicit Differentiation](https://mlsanity.com/paper/1911.02590/) (2019)
- [Strategic Classification](https://mlsanity.com/paper/1506.06980/) (2015)
- [Hyperparameter optimization with approximate gradient](https://mlsanity.com/paper/1602.02355/) (2016)
- [On Differentiating Parameterized Argmin and Argmax Problems with Application to Bi-level Optimization](https://mlsanity.com/paper/1607.05447/) (2016)
- [The Social Cost of Strategic Classification](https://mlsanity.com/paper/1808.08460/) (2018)
- [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)
- [Inadequacies of Large Language Model Benchmarks in the Era of Generative Artificial Intelligence](https://mlsanity.com/paper/2402.09880/) (2024)
- [Strategic Classification Made Practical](https://mlsanity.com/paper/2103.01826/) (2021)
- [PAC-Learning for Strategic Classification](https://mlsanity.com/paper/2012.03310/) (2020)
- [A Closer Look at Deep Learning Methods on Tabular Datasets](https://mlsanity.com/paper/2407.00956/) (2024)
- [The Role of Randomness and Noise in Strategic Classification](https://mlsanity.com/paper/2005.08377/) (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)
- [Beyond backpropagation: bilevel optimization through implicit differentiation and equilibrium propagation](https://mlsanity.com/paper/2205.03076/) (2022)
- [Strategic Classification with Graph Neural Networks](https://mlsanity.com/paper/2205.15765/) (2022)
- [One-Shot Strategic Classification Under Unknown Costs](https://mlsanity.com/paper/2311.02761/) (2023)
- [Bayesian Strategic Classification](https://mlsanity.com/paper/2402.08758/) (2024)
- [Optimal Classification under Performative Distribution Shift](https://mlsanity.com/paper/2411.02023/) (2024)
- [Meta Mirror Descent: Optimiser Learning for Fast Convergence](https://mlsanity.com/paper/2203.02711/) (2022)
- [Strategic Classification with Randomised Classifiers](https://mlsanity.com/paper/2502.01313/) (2025)
- [Strategic Classification with Non-Linear Classifiers](https://mlsanity.com/paper/2505.23443/) (2025)
- [Nonlinear Performative Prediction](https://mlsanity.com/paper/2509.01139/) (2025)

## Abstract (arXiv)

Algorithmic developments in Strategic Classification have been mostly limited to linear classifiers in settings where the best response has a closed-form solution or can be easily approximated. While some work has explored the role of non-linear classifiers in strategic settings, progress in this direction is impeded by the computational intractability of the strategic behaviour. Addressing this, we present a novel method for approximating the best response by exploiting Lagrangian duality. By reformulating the strategic response as a constrained optimisation problem, we can construct a Lagrangian that is amenable to first order optimisation methods. This approach reproduces closed-form strategic behaviour in linear settings and can be straight-forwardly applied to non-linear settings. We show how the Implicit Function Theorem can be used in conjunction with our proposed response formulation during classifier learning to compute the total gradient of the loss. This connects the classifier parameters directly to the consequent strategic behaviour, yielding a novel training algorithm that can exploit this relationship. Experimental evaluation shows that the resulting models achieve improved strategic accuracy on common machine learning datasets.