Computing Strategic Responses to Non-Linear Classifiers

2025-11-26

AI Summary

This paper addresses the problem of computing optimal responses in strategic classification, where classifier deployment induces strategic user behavior that shifts the data distribution. Existing methods are largely restricted to linear models and fail to yield tractable solutions for nonlinear classifiers. To overcome this limitation, we propose a novel framework based on Lagrangian dual optimization of a surrogate objective, unifying optimal-response computation with classifier training. Our approach exactly recovers known optimal solutions in the linear case and exposes theoretical shortcomings of several prior methods. For the first time, it enables scalable, differentiable estimation of optimal responses for nonlinear models—including kernel SVMs and neural networks. Experiments demonstrate that our method significantly improves model robustness and generalization under strategic manipulation, establishing the first general-purpose, practical paradigm for nonlinear strategic classification.

Technology Category

• Search and Optimization: Learning to Search
• Machine Learning: Adversarial Learning & Robustness
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• Computing best responses for non-linear classifiers in strategic classification settings
• Addressing distribution shifts caused by strategic agent behavior after classifier deployment
• Overcoming limitations of existing methods focused primarily on linear classification scenarios

Innovation

• Computes best responses using Lagrangian dual optimization
• Reproduces linear classifier responses and identifies weaknesses
• Applies to non-linear classifiers for evaluation and training