Non-Linear Strategic Classification Made Practical

2026-06-26

AI Summary

This work addresses the challenge of deploying nonlinear classifiers in strategic classification settings, where computing agents’ optimal responses is typically intractable. The authors model an agent’s strategic response as a constrained optimization problem and leverage Lagrangian duality to reformulate it into a first-order differentiable form. By applying the implicit function theorem, they explicitly establish gradient-based relationships between classifier parameters and strategic behaviors. This approach enables, for the first time, scalable end-to-end training of nonlinear strategic classifiers and provides a unified framework for approximating optimal responses in both linear and nonlinear settings. Experimental results on multiple benchmark datasets demonstrate significant improvements in strategic accuracy, confirming the method’s effectiveness and practical utility.

Abstract

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.

Problem

• Strategic Classification
• Non-Linear Classifiers
• Best Response
• Computational Intractability
• Strategic Behavior

Innovation

• Strategic Classification
• Non-linear Classifiers
• Lagrangian Duality
• Implicit Function Theorem
• Best Response Approximation