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On Classification of Strategic Agents Who Can Both Game and Improve

Authors Saba Ahmadi, Hedyeh Beyhaghi, Avrim Blum, Keziah Naggita



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Author Details

Saba Ahmadi
  • Toyota Technological Institute at Chicago, IL, USA
Hedyeh Beyhaghi
  • Carnegie Mellon University, Pittsburgh, PA, USA
Avrim Blum
  • Toyota Technological Institute at Chicago, IL, USA
Keziah Naggita
  • Toyota Technological Institute at Chicago, IL, USA

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Saba Ahmadi, Hedyeh Beyhaghi, Avrim Blum, and Keziah Naggita. On Classification of Strategic Agents Who Can Both Game and Improve. In 3rd Symposium on Foundations of Responsible Computing (FORC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 218, pp. 3:1-3:22, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.FORC.2022.3

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic mechanism design
  • Theory of computation → Sample complexity and generalization bounds
Keywords
  • Strategic Classification
  • Social Welfare
  • Learning

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References

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