Computing Strategic Responses to Non-Linear Classifiers

TL;DR

This paper introduces a novel method for computing strategic responses in non-linear classifiers, addressing a key challenge in strategic classification by optimizing the Lagrangian dual to handle complex models.

Contribution

It presents a new approach for calculating best responses in non-linear classifiers, extending strategic classification methods beyond linear models.

Findings

Method reproduces best responses in linear settings

Applicable to non-linear classifiers for evaluation and training

Identifies weaknesses in existing approaches

Abstract

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.