Advancing Subgroup Fairness via Sleeping Experts

Authors Avrim Blum, Thodoris Lykouris

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Avrim Blum
  • Toyota Technological Institute at Chicago, IL, United States
Thodoris Lykouris
  • Microsoft Research NYC, United States


The authors would like to thank Suriya Gunasekar for various useful discussions during the initial stages of this work and Manish Raghavan for offering comments in a preliminary version of the work.

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Avrim Blum and Thodoris Lykouris. Advancing Subgroup Fairness via Sleeping Experts. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 55:1-55:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


We study methods for improving fairness to subgroups in settings with overlapping populations and sequential predictions. Classical notions of fairness focus on the balance of some property across different populations. However, in many applications the goal of the different groups is not to be predicted equally but rather to be predicted well. We demonstrate that the task of satisfying this guarantee for multiple overlapping groups is not straightforward and show that for the simple objective of unweighted average of false negative and false positive rate, satisfying this for overlapping populations can be statistically impossible even when we are provided predictors that perform well separately on each subgroup. On the positive side, we show that when individuals are equally important to the different groups they belong to, this goal is achievable; to do so, we draw a connection to the sleeping experts literature in online learning. Motivated by the one-sided feedback in natural settings of interest, we extend our results to such a feedback model. We also provide a game-theoretic interpretation of our results, examining the incentives of participants to join the system and to provide the system full information about predictors they may possess. We end with several interesting open problems concerning the strength of guarantees that can be achieved in a computationally efficient manner.

Subject Classification

ACM Subject Classification
  • Theory of computation → Online learning algorithms
  • Online learning
  • Fairness
  • Game theory


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  1. Alekh Agarwal, Alina Beygelzimer, Miroslav Dudík, John Langford, and Hanna Wallach. A reductions approach to fair classification. arXiv preprint, 2018. URL:
  2. Itai Ashlagi, Felix Fischer, Ian A. Kash, and Ariel D. Procaccia. Mix and match: A strategyproof mechanism for multi-hospital kidney exchange. Games and Economic Behavior, 91, May 2013. URL:
  3. Itai Ashlagi and Alvin E Roth. Free riding and participation in large scale, multi-hospital kidney exchange. Theoretical Economics, 9(3):817-863, 2014. Google Scholar
  4. Baruch Awerbuch and Yishay Mansour. Adapting to a reliable network path. In Proceedings of the twenty-second annual symposium on Principles of distributed computing (PODC), 2003. Google Scholar
  5. Yahav Bechavod, Katrina Ligett, Aaron Roth, Bo Waggoner, and Zhiwei Steven Wu. Equal Opportunity in Online Classification with Partial Feedback. In 33rd Annual Conference on Neural Information Processing Systems (NeurIPS), 2019. Google Scholar
  6. Avrim Blum. Empirical support for winnow and weighted-majority algorithms: Results on a calendar scheduling domain. Machine Learning, 26(1):5-23, 1997. Google Scholar
  7. Avrim Blum, Suriya Gunasekar, Thodoris Lykouris, and Nathan Srebro. On preserving non-discrimination when combining expert advice. In 32nd Annual Conference on Neural Information Processing Systems (NeurIPS), 2018. URL:
  8. Avrim Blum and Yishay Mansour. From external to internal regret. Journal of Machine Learning Research (JMLR), 2007. Google Scholar
  9. Toon Calders, Faisal Kamiran, and Mykola Pechenizkiy. Building Classifiers with Independency Constraints. In IEEE International Conference on Data Mining (ICDM), 2009. Google Scholar
  10. L Elisa Celis, Sayash Kapoor, Farnood Salehi, and Nisheeth K Vishnoi. An Algorithmic Framework to Control Bias in Bandit-based Personalization. arXiv preprint, 2018. URL:
  11. Nicolo Cesa-Bianchi, Gábor Lugosi, and Gilles Stoltz. Minimizing regret with label efficient prediction. IEEE Transactions on Information Theory, 51(6):2152-2162, 2005. Google Scholar
  12. Alexandra Chouldechova. Fair prediction with disparate impact: A study of bias in recidivism prediction instruments. Big data, 5(2):153-163, 2017. Google Scholar
  13. Sam Corbett-Davies and Sharad Goel. The measure and mismeasure of fairness: A critical review of fair machine learning. arXiv preprint, 2018. URL:
  14. Cynthia Dwork, Moritz Hardt, Toniann Pitassi, Omer Reingold, and Richard Zemel. Fairness Through Awareness. In Proceedings of the 3rd Innovations in Theoretical Computer Science Conference (ITCS), 2012. Google Scholar
  15. Michael Feldman, Sorelle A. Friedler, John Moeller, Carlos Scheidegger, and Suresh Venkatasubramanian. Certifying and Removing Disparate Impact. In Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD), 2015. Google Scholar
  16. Yoav Freund and Robert E Schapire. A Decision-Theoretic Generalization of On-Line Learning and an Application to Boosting. J. Comput. Syst. Sci., 1997. Google Scholar
  17. Yoav Freund, Robert E Schapire, Yoram Singer, and Manfred K Warmuth. Using and combining predictors that specialize. In Proceedings of the twenty-ninth annual ACM symposium on Theory of computing (STOC), pages 334-343. ACM, 1997. Google Scholar
  18. Pierre Gaillard, Gilles Stoltz, and Tim Van Erven. A second-order bound with excess losses. In Conference on Learning Theory (COLT), 2014. Google Scholar
  19. Stephen Gillen, Christopher Jung, Michael Kearns, and Aaron Roth. Online Learning with an Unknown Fairness Metric. In Advances in Neural Information Processing Systems (NeurIPS), 2018. Google Scholar
  20. Eyal Gofer and Yishay Mansour. Lower bounds on individual sequence regret. Machine Learning, 103(1):1-26, 2016. Google Scholar
  21. Swati Gupta and Vijay Kamble. Individual Fairness in Hindsight. In Proceedings of the 2019 ACM Conference on Economics and Computation (EC), 2019. Google Scholar
  22. Moritz Hardt, Eric Price, and Nathan Srebro. Equality of opportunity in supervised learning. In Advances in neural information processing systems (NIPS), 2016. Google Scholar
  23. Ursula Hebert-Johnson, Michael Kim, Omer Reingold, and Guy Rothblum. Multicalibration: Calibration for the (Computationally-Identifiable) Masses. In Proceedings of the 35th International Conference on Machine Learning (ICML), 2018. Google Scholar
  24. David P. Helmbold, Nick Littlestone, and Philip M. Long. Apple Tasting and Nearly One-Sided Learning. In 33rd Annual Symposium on Foundations of Computer Science (FOCS), 1992. Google Scholar
  25. Matthew Joseph, Michael Kearns, Jamie H Morgenstern, and Aaron Roth. Fairness in learning: Classic and contextual bandits. In Advances in Neural Information Processing Systems (NIPS), 2016. Google Scholar
  26. Michael Kearns, Seth Neel, Aaron Roth, and Zhiwei Steven Wu. Preventing Fairness Gerrymandering: Auditing and Learning for Subgroup Fairness. In In Proceedings of the 35th International Conference on Machine Learning (ICML), 2018. Google Scholar
  27. Niki Kilbertus, Mateo Rojas Carulla, Giambattista Parascandolo, Moritz Hardt, Dominik Janzing, and Bernhard Schölkopf. Avoiding discrimination through causal reasoning. In Advances in Neural Information Processing Systems (NIPS), 2017. Google Scholar
  28. Michael P. Kim, Amirata Ghorbani, and James Zou. Multiaccuracy: Black-Box Post-Processing for Fairness in Classification. In Proceedings of the 2019 AAAI/ACM Conference on AI, Ethics, and Society, AIES '19, 2019. URL:
  29. Michael P. Kim, Omer Reingold, and Guy N. Rothblum. Fairness Through Computationally-bounded Awareness. In Proceedings of the 32Nd International Conference on Neural Information Processing Systems (NeurIPS), 2018. URL:
  30. Jon Kleinberg, Himabindu Lakkaraju, Jure Leskovec, Jens Ludwig, and Sendhil Mullainathan. Human decisions and machine predictions. The quarterly journal of economics, 133(1):237-293, 2017. Google Scholar
  31. Jon M. Kleinberg, Sendhil Mullainathan, and Manish Raghavan. Inherent Trade-Offs in the Fair Determination of Risk Scores. In Innovations of Theoretical Computer Science (ITCS), 2017. Google Scholar
  32. Nick Littlestone and Manfred K. Warmuth. The Weighted Majority Algorithm. Inf. Comput., 108(2):212-261, February 1994. URL:
  33. Lydia T. Liu, Sarah Dean, Esther Rolf, Max Simchowitz, and Moritz Hardt. Delayed Impact of Fair Machine Learning. 35th International Conference on Machine Learning (ICML), 2018. Google Scholar
  34. Yang Liu, Goran Radanovic, Christos Dimitrakakis, Debmalya Mandal, and David C Parkes. Calibrated Fairness in Bandits. In Workshop on Fairness, Accountability, and Transparency in Machine Learning (FAT-ML), 2017. Google Scholar
  35. Haipeng Luo and Robert E. Schapire. Achieving All with No Parameters: AdaNormalHedge. In Proceedings of The 28th Conference on Learning Theory (COLT), 2015. URL:
  36. Manish Raghavan, Aleksandrs Slivkins, Jennifer Vaughan Wortman, and Zhiwei Steven Wu. The Externalities of Exploration and How Data Diversity Helps Exploitation. In Proceedings of the 31st Conference On Learning Theory (COLT), 2018. Google Scholar
  37. Alvin E. Roth, Tayfun Sönmez, and M. Utku Ünver. Efficient Kidney Exchange: Coincidence of Wants in Markets with Compatibility-Based Preferences. American Economic Review, 97(3):828-851, June 2007. URL: