ABSTRACT
Resource allocation problems are a fundamental domain in which to evaluate the fairness properties of algorithms. The trade-offs between fairness and utilization have a long history in this domain. A recent line of work has considered fairness questions for resource allocation when the demands for the resource are distributed across multiple groups and drawn from probability distributions. In such cases, a natural fairness requirement is that individuals from different groups should have (approximately) equal probabilities of receiving the resource. A largely open question in this area has been to bound the gap between the maximum possible utilization of the resource and the maximum possible utilization subject to this fairness condition.
Here, we obtain some of the first provable upper bounds on this gap. We obtain an upper bound for arbitrary distributions, as well as much stronger upper bounds for specific families of distributions that are typically used to model levels of demand. In particular, we find --- somewhat surprisingly --- that there are natural families of distributions (including Exponential and Weibull) for which the gap is non-existent: it is possible to simultaneously achieve maximum utilization and the given notion of fairness. Finally, we show that for power-law distributions, there is a non-trivial gap between the solutions, but this gap can be bounded by a constant factor independent of the parameters of the distribution.
References
- Stephen Boyd and Lieven Vandenberghe. 2004. Convex Optimization. Cambridge University Press.Google Scholar
- Dah-Ming Chiu and Raj Jain. 1989. Analysis of the Increase and Decrease Algorithms for Congestion Avoidance in Computer Networks. Comput. Netw. ISDN Syst. 17, 1 (June 1989), 1--14. Google Scholar
Digital Library
- Dah Ming Chiu and Raj Jain. 1989. Analysis of the increase and decrease algorithms for congestion avoidance in computer networks. Computer Networks and ISDN Systems 17 (06 1989), 1--14. Google Scholar
Digital Library
- Aaron Clauset. 2018. Trends and fluctuations in the severity of interstate wars. Science Advances 4, 2 (2018). arXiv:https://advances.sciencemag.org/content/4/2/eaao3580.full.pdf Google Scholar
Cross Ref
- Aaron Clauset, Cosma Rohilla Shalizi, and M. E. J. Newman. 2007. Power-law distributions in empirical data. arXiv e-prints, Article arXiv:0706.1062 (Jun 2007), arXiv:0706.1062 pages. arXiv:physics.data-an/0706.1062Google Scholar
- A. Demers, S. Keshav, and S. Shenker. 1989. Analysis and Simulation of a Fair Queueing Algorithm. SIGCOMM Comput. Commun. Rev. 19, 4 (Aug. 1989), 1--12. Google Scholar
Digital Library
- Hadi Elzayn, Shahin Jabbari, Christopher Jung, Michael Kearns, Seth Neel, Aaron Roth, and Zachary Schutzman. 2019. Fair Algorithms for Learning in Allocation Problems. Proceedings of the Conference on Fairness, Accountability, and Transparency- FAT*'19 (2019). Google Scholar
Digital Library
- Danielle Ensign, Sorelle A. Friedler, Scott Neville, Carlos Scheidegger, and Suresh Venkatasubramanian. 2018. Runaway Feedback Loops in Predictive Policing. In Proceedings of the 1st Conference on Fairness, Accountability and Transparency (Proceedings of Machine Learning Research), Sorelle A. Friedler and Christo Wilson (Eds.), Vol. 81. PMLR, New York, NY, USA, 160--171. http://proceedings.mlr.press/v81/ensign18a.htmlGoogle Scholar
- Ricardo Estrada and Miroslav Pavlovic. 2016. L'Hôpital's Monotone rule, Gromov's theorem, and operations that preserve the monotonicity of quotients. Publications de l'Institut Mathematique 101(115), 2017, 11--24 101 (12 2016). Google Scholar
Cross Ref
- Virginia Eubanks. 2018. Automating Inequality. St. Martin's Press.Google Scholar
- Kuzman Ganchev, Michael Kearns, Yuriy Nevmyvaka, and Jennifer Wortman Vaughan. 2009. Censored exploration and the dark pool problem. In Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence. AUAI Press, 185--194.Google Scholar
Digital Library
- Jeffrey M. Jaffe. 1981. Bottleneck flow control. IEEE Transactions on Communications 29 (1981), 954--962.Google Scholar
Cross Ref
- Frank P Kelly, Aman K Maulloo, and David KH Tan. 1998. Rate control for communication networks: shadow prices, proportional fairness and stability. Journal of the Operational Research society 49, 3 (1998), 237--252.Google Scholar
Cross Ref
- Ariel D. Procaccia. 2013. Cake cutting: not just child's play. Commun. ACM 56, 7 (2013), 78--87. Google Scholar
Digital Library
- Yanyan Wang, Vicki M. Bier, and Baiqing Sun. [n. d.]. Measuring and Achieving Equity in Multiperiod Emergency Material Allocation. Risk Analysis 0, 0 ([n. d.]). arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1111/risa.13342 Google Scholar
Cross Ref
Supplemental Material
Available for Download
Index Terms
Fairness and utilization in allocating resources with uncertain demand




Comments