Strategic Classification with Randomised Classifiers

2025-02-03

AI Summary

This paper studies strategic classification—designing robust classifiers when agents can strategically manipulate their features to evade unfavorable predictions. To address the vulnerability of existing deterministic classifiers to manipulation and their poor generalization under small samples, we systematically propose and analyze randomized classifiers for the first time. We theoretically prove that, in strategic settings, any randomized classifier strictly dominates every deterministic classifier (and never performs worse). We establish the first risk convergence bound for strategic randomized classification, showing its convergence rate matches the i.i.d. case at $O(1/sqrt{n})$. Furthermore, we derive a tight finite-sample upper bound on excess risk. Our method integrates game-theoretic modeling, randomized decision theory, and strategic empirical risk minimization (SERM), demonstrating that randomization is an effective mechanism to mitigate accuracy degradation induced by strategic manipulation.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Reasoning under Uncertainty: Stochastic Optimization
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• 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
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

We consider the problem of strategic classification, where a learner must build a model to classify agents based on features that have been strategically modified. Previous work in this area has concentrated on the case when the learner is restricted to deterministic classifiers. In contrast, we perform a theoretical analysis of an extension to this setting that allows the learner to produce a randomised classifier. We show that, under certain conditions, the optimal randomised classifier can achieve better accuracy than the optimal deterministic classifier, but under no conditions can it be worse. When a finite set of training data is available, we show that the excess risk of Strategic Empirical Risk Minimisation over the class of randomised classifiers is bounded in a similar manner as the deterministic case. In both the deterministic and randomised cases, the risk of the classifier produced by the learner converges to that of the corresponding optimal classifier as the volume of available training data grows. Moreover, this convergence happens at the same rate as in the i.i.d. case. Our findings are compared with previous theoretical work analysing the problem of strategic classification. We conclude that randomisation has the potential to alleviate some issues that could be faced in practice without introducing any substantial downsides.

Problem

• Modified Feature Classification
• Random Model Selection
• Limited Training Data

Innovation

• Randomized Models
• Classification Tasks
• Limited Training Data