Strategic Classification under Unknown Personalized Manipulation

TL;DR

This paper investigates the fundamental limits of learning in strategic classification settings where agents can manipulate features differently and unpredictably, providing mistake bounds and sample complexity results for various information scenarios.

Contribution

It introduces a formal model for personalized, unknown manipulations in strategic classification and derives mistake bounds and sample complexity in different observational settings.

Findings

Mistake bounds and PAC sample complexity are established for ball manipulations.

Lower bounds are shown for non-ball manipulations even when both original and manipulated features are observed.

The work extends understanding of learning limits under personalized, unknown strategic manipulations.

Abstract

We study the fundamental mistake bound and sample complexity in the strategic classification, where agents can strategically manipulate their feature vector up to an extent in order to be predicted as positive. For example, given a classifier determining college admission, student candidates may try to take easier classes to improve their GPA, retake SAT and change schools in an effort to fool the classifier. Ball manipulations are a widely studied class of manipulations in the literature, where agents can modify their feature vector within a bounded radius ball. Unlike most prior work, our work considers manipulations to be personalized, meaning that agents can have different levels of manipulation abilities (e.g., varying radii for ball manipulations), and unknown to the learner. We formalize the learning problem in an interaction model where the learner first deploys a classifier and the agent manipulates the feature vector within their manipulation set to game the deployed classifier. We investigate various scenarios in terms of the information available to the learner during the interaction, such as observing the original feature vector before or after deployment, observing the manipulated feature vector, or not seeing either the original or the manipulated feature vector. We begin by providing online mistake bounds and PAC sample complexity in these scenarios for ball manipulations. We also explore non-ball manipulations and show that, even in the simplest scenario where both the original and the manipulated feature vectors are revealed, the mistake bounds and sample complexity are lower bounded by $\Omega(|H|)$ when the target function belongs to a known class $H$.