Strategic Classification with Non-Linear Classifiers

TL;DR

This paper investigates how strategic user behavior impacts non-linear classifiers, revealing that non-linearity can alter class complexity and that universal approximation properties may not hold in strategic environments.

Contribution

It extends strategic classification analysis from linear to non-linear classifiers, showing how non-linearity influences decision boundaries and model complexity.

Findings

Strategic behavior can increase or decrease class complexity in non-linear classifiers.

Universal approximators may lose their universality in strategic settings.

Performance gaps can occur even with unrestricted model classes.

Abstract

In strategic classification, the standard supervised learning setting is extended to support the notion of strategic user behavior in the form of costly feature manipulations made in response to a classifier. While standard learning supports a broad range of model classes, the study of strategic classification has, so far, been dedicated mostly to linear classifiers. This work aims to expand the horizon by exploring how strategic behavior manifests under non-linear classifiers and what this implies for learning. We take a bottom-up approach showing how non-linearity affects decision boundary points, classifier expressivity, and model class complexity. Our results show how, unlike the linear case, strategic behavior may either increase or decrease effective class complexity, and that the complexity decrease may be arbitrarily large. Another key finding is that universal approximators (e.g., neural nets) are no longer universal once the environment is strategic. We demonstrate empirically how this can create performance gaps even on an unrestricted model class.