Strategic Classification with Non-Linear Classifiers

2025-05-29

AI Summary

This paper addresses strategic feature manipulation—where users incur costs to alter input features to improve classifier predictions—in strategic classification settings. We systematically investigate the learning dynamics and performance limits of nonlinear classifiers (e.g., neural networks) under such strategic behavior. Using game-theoretic modeling, decision boundary analysis, theoretical derivation for nonlinear models, and empirical evaluation, we establish that even universal approximators—such as deep neural networks—suffer significant expressive degradation under strategic manipulation: their classical universal approximation property fails in strategic environments. This reveals a fundamental tension between model capacity and strategic robustness in strategic machine learning. Crucially, we derive the first rigorous theoretical lower bound on the strategic robustness of nonlinear classifiers, thereby closing a critical theoretical gap beyond the linear-regime assumptions prevalent in prior work.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Game Theory and Economic Paradigms: Adversarial Learning
• Computer Vision: Adversarial Attacks & Robustness

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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 classes complexity. A 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.

Problem

• Explores strategic behavior under non-linear classifiers
• Investigates impact on decision boundaries and model complexity
• Shows universal approximators fail in strategic environments

Innovation

• Explores strategic behavior with non-linear classifiers
• Analyzes decision boundary and classifier expressivity
• Shows universal approximators fail in strategic environments