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DOI: 10.4230/LIPIcs.FORC.2023.5

Setting Fair Incentives to Maximize Improvement

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

Published in: LIPIcs, Volume 256, 4th Symposium on Foundations of Responsible Computing (FORC 2023)

Abstract

We consider the problem of helping agents improve by setting goals. Given a set of target skill levels, we assume each agent will try to improve from their initial skill level to the closest target level within reach (or do nothing if no target level is within reach). We consider two models: the common improvement capacity model, where agents have the same limit on how much they can improve, and the individualized improvement capacity model, where agents have individualized limits. Our goal is to optimize the target levels for social welfare and fairness objectives, where social welfare is defined as the total amount of improvement, and we consider fairness objectives when the agents belong to different underlying populations. We prove algorithmic, learning, and structural results for each model. A key technical challenge of this problem is the non-monotonicity of social welfare in the set of target levels, i.e., adding a new target level may decrease the total amount of improvement; agents who previously tried hard to reach a distant target now have a closer target to reach and hence improve less. This especially presents a challenge when considering multiple groups because optimizing target levels in isolation for each group and outputting the union may result in arbitrarily low improvement for a group, failing the fairness objective. Considering these properties, we provide algorithms for optimal and near-optimal improvement for both social welfare and fairness objectives. These algorithmic results work for both the common and individualized improvement capacity models. Furthermore, despite the non-monotonicity property and interference of the target levels, we show a placement of target levels exists that is approximately optimal for the social welfare of each group. Unlike the algorithmic results, this structural statement only holds in the common improvement capacity model, and we illustrate counterexamples of this result in the individualized improvement capacity model. Finally, we extend our algorithms to learning settings where we have only sample access to the initial skill levels of agents.

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Saba Ahmadi, Hedyeh Beyhaghi, Avrim Blum, and Keziah Naggita. Setting Fair Incentives to Maximize Improvement. In 4th Symposium on Foundations of Responsible Computing (FORC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 256, pp. 5:1-5:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{ahmadi_et_al:LIPIcs.FORC.2023.5,
  author =	{Ahmadi, Saba and Beyhaghi, Hedyeh and Blum, Avrim and Naggita, Keziah},
  title =	{{Setting Fair Incentives to Maximize Improvement}},
  booktitle =	{4th Symposium on Foundations of Responsible Computing (FORC 2023)},
  pages =	{5:1--5:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-272-3},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{256},
  editor =	{Talwar, Kunal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2023.5},
  URN =		{urn:nbn:de:0030-drops-179261},
  doi =		{10.4230/LIPIcs.FORC.2023.5},
  annote =	{Keywords: Algorithmic Fairness, Learning for Strategic Behavior, Incentivizing Improvement}
}

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DOI: 10.4230/LIPIcs.FORC.2022.3

On Classification of Strategic Agents Who Can Both Game and Improve

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

Published in: LIPIcs, Volume 218, 3rd Symposium on Foundations of Responsible Computing (FORC 2022)

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.

Cite as

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)

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@InProceedings{ahmadi_et_al:LIPIcs.FORC.2022.3,
  author =	{Ahmadi, Saba and Beyhaghi, Hedyeh and Blum, Avrim and Naggita, Keziah},
  title =	{{On Classification of Strategic Agents Who Can Both Game and Improve}},
  booktitle =	{3rd Symposium on Foundations of Responsible Computing (FORC 2022)},
  pages =	{3:1--3:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-226-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{218},
  editor =	{Celis, L. Elisa},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2022.3},
  URN =		{urn:nbn:de:0030-drops-165269},
  doi =		{10.4230/LIPIcs.FORC.2022.3},
  annote =	{Keywords: Strategic Classification, Social Welfare, Learning}
}

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Setting Fair Incentives to Maximize Improvement

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On Classification of Strategic Agents Who Can Both Game and Improve

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