On classification of strategic agents who can both game and improve

TL;DR

This paper studies classifying agents who can both game and improve, proposing algorithms and proving hardness results for maximizing true positives while controlling false positives in discrete and linear models.

Contribution

It introduces models and algorithms for classifying strategic agents who can improve or game, along with hardness proofs and learning extensions.

Findings

Efficient algorithm for maximizing true positives with zero false positives in discrete model.

Hardness results for maximizing true positives with nonzero false positives.

Algorithm to find linear classifiers that classify all agents correctly and induce improvement.

Abstract

In this work, we consider classification of agents who can both game and improve. For example, people wishing to get a loan may be able to take some actions that increase their perceived credit-worthiness and others that also increase their true credit-worthiness. A decision-maker would like to define a classification rule with few false-positives (does not give out many bad loans) while yielding many true positives (giving out many good loans), which includes encouraging agents to improve to become true positives if possible. We consider two models for this problem, a general discrete model and a linear model, and prove algorithmic, learning, and hardness results for each. For the general discrete model, we give an efficient algorithm for the problem of maximizing the number of true positives subject to no false positives, and show how to extend this to a partial-information learning setting. We also show hardness for the problem of maximizing the number of true positives subject to a nonzero bound on the number of false positives, and that this hardness holds even for a finite-point version of our linear model. We also show that maximizing the number of true positives subject to no false positive is NP-hard in our full linear model. We additionally provide an algorithm that determines whether there exists a linear classifier that classifies all agents accurately and causes all improvable agents to become qualified, and give additional results for low-dimensional data.