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DOI: 10.4230/LIPIcs.FORC.2021.6

Lexicographically Fair Learning: Algorithms and Generalization

Authors: Emily Diana, Wesley Gill, Ira Globus-Harris, Michael Kearns, Aaron Roth, and Saeed Sharifi-Malvajerdi

Published in: LIPIcs, Volume 192, 2nd Symposium on Foundations of Responsible Computing (FORC 2021)

Abstract

We extend the notion of minimax fairness in supervised learning problems to its natural conclusion: lexicographic minimax fairness (or lexifairness for short). Informally, given a collection of demographic groups of interest, minimax fairness asks that the error of the group with the highest error be minimized. Lexifairness goes further and asks that amongst all minimax fair solutions, the error of the group with the second highest error should be minimized, and amongst all of those solutions, the error of the group with the third highest error should be minimized, and so on. Despite its naturalness, correctly defining lexifairness is considerably more subtle than minimax fairness, because of inherent sensitivity to approximation error. We give a notion of approximate lexifairness that avoids this issue, and then derive oracle-efficient algorithms for finding approximately lexifair solutions in a very general setting. When the underlying empirical risk minimization problem absent fairness constraints is convex (as it is, for example, with linear and logistic regression), our algorithms are provably efficient even in the worst case. Finally, we show generalization bounds - approximate lexifairness on the training sample implies approximate lexifairness on the true distribution with high probability. Our ability to prove generalization bounds depends on our choosing definitions that avoid the instability of naive definitions.

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Emily Diana, Wesley Gill, Ira Globus-Harris, Michael Kearns, Aaron Roth, and Saeed Sharifi-Malvajerdi. Lexicographically Fair Learning: Algorithms and Generalization. In 2nd Symposium on Foundations of Responsible Computing (FORC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 192, pp. 6:1-6:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{diana_et_al:LIPIcs.FORC.2021.6,
  author =	{Diana, Emily and Gill, Wesley and Globus-Harris, Ira and Kearns, Michael and Roth, Aaron and Sharifi-Malvajerdi, Saeed},
  title =	{{Lexicographically Fair Learning: Algorithms and Generalization}},
  booktitle =	{2nd Symposium on Foundations of Responsible Computing (FORC 2021)},
  pages =	{6:1--6:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-187-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{192},
  editor =	{Ligett, Katrina and Gupta, Swati},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2021.6},
  URN =		{urn:nbn:de:0030-drops-138748},
  doi =		{10.4230/LIPIcs.FORC.2021.6},
  annote =	{Keywords: Fair Learning, Lexicographic Fairness, Online Learning, Game Theory}
}

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DOI: 10.4230/LIPIcs.ITCS.2020.31

A New Analysis of Differential Privacy’s Generalization Guarantees

Authors: Christopher Jung, Katrina Ligett, Seth Neel, Aaron Roth, Saeed Sharifi-Malvajerdi, and Moshe Shenfeld

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

Abstract

We give a new proof of the "transfer theorem" underlying adaptive data analysis: that any mechanism for answering adaptively chosen statistical queries that is differentially private and sample-accurate is also accurate out-of-sample. Our new proof is elementary and gives structural insights that we expect will be useful elsewhere. We show: 1) that differential privacy ensures that the expectation of any query on the conditional distribution on datasets induced by the transcript of the interaction is close to its expectation on the data distribution, and 2) sample accuracy on its own ensures that any query answer produced by the mechanism is close to the expectation of the query on the conditional distribution. This second claim follows from a thought experiment in which we imagine that the dataset is resampled from the conditional distribution after the mechanism has committed to its answers. The transfer theorem then follows by summing these two bounds, and in particular, avoids the "monitor argument" used to derive high probability bounds in prior work. An upshot of our new proof technique is that the concrete bounds we obtain are substantially better than the best previously known bounds, even though the improvements are in the constants, rather than the asymptotics (which are known to be tight). As we show, our new bounds outperform the naive "sample-splitting" baseline at dramatically smaller dataset sizes compared to the previous state of the art, bringing techniques from this literature closer to practicality.

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Christopher Jung, Katrina Ligett, Seth Neel, Aaron Roth, Saeed Sharifi-Malvajerdi, and Moshe Shenfeld. A New Analysis of Differential Privacy’s Generalization Guarantees. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 31:1-31:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{jung_et_al:LIPIcs.ITCS.2020.31,
  author =	{Jung, Christopher and Ligett, Katrina and Neel, Seth and Roth, Aaron and Sharifi-Malvajerdi, Saeed and Shenfeld, Moshe},
  title =	{{A New Analysis of Differential Privacy’s Generalization Guarantees}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{31:1--31:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.31},
  URN =		{urn:nbn:de:0030-drops-117165},
  doi =		{10.4230/LIPIcs.ITCS.2020.31},
  annote =	{Keywords: Differential Privacy, Adaptive Data Analysis, Transfer Theorem}
}

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Documents authored by Sharifi-Malvajerdi, Saeed

Lexicographically Fair Learning: Algorithms and Generalization

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A New Analysis of Differential Privacy’s Generalization Guarantees

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