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We consider the problem of dividing limited resources to individuals arriving over T rounds. Each round has a random number of individuals arrive, and individuals can be characterized by their type (i.e. preferences over the different resources). A standard notion of 'fairness' in this setting is that an allocation simultaneously satisfy envy-freeness and efficiency. For divisible resources, when the number of individuals of each type are known upfront, the above desiderata are simultaneously achievable for a large class of utility functions. However, in an online setting when the number of individuals of each type are only revealed round by round, no policy can guarantee these desiderata simultaneously.We show that in the online setting, the two desired properties (envy-freeness and efficiency) are in direct contention, in that any algorithm achieving additive counterfactual envy-freeness up to a factor of LT necessarily suffers a efficiency loss of at least 1 / LT. We complement this uncertainty principle with a simple algorithm, Guarded-Hope, which allocates resources based on an adaptive threshold policy and is able to achieve any fairness-efficiency point on this frontier.
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Online Fair Allocation of Perishable Resources
We consider a practically motivated variant of the canonical online fair allocation problem: a decision-maker has a budget of resources to allocate over a fixed number of rounds. Each round sees a random number of arrivals, and the decision-maker must commit to an allocation for these individuals before moving on to the next round. In contrast to prior work, we consider a setting in which resources are perishable and individuals' utilities are potentially non-linear (e.g., goods exhibit complementarities). The goal is to construct a sequence of allocations that is envy-free and efficient. We design an algorithm that takes as input (i) a prediction of the perishing order, and (ii) a desired bound on envy. Given the remaining budget in each period, the algorithm uses forecasts of future demand and perishing to adaptively choose one of two carefully constructed guardrail quantities. We characterize conditions under which our algorithm achieves the optimal envy-efficiency Pareto frontier. We moreover demonstrate its strong numerical performance using data from a partnering food bank.
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- PAR ID:
- 10528652
- Publisher / Repository:
- ACM
- Date Published:
- Journal Name:
- ACM SIGMETRICS Performance Evaluation Review
- Volume:
- 51
- Issue:
- 1
- ISSN:
- 0163-5999
- Page Range / eLocation ID:
- 55 to 56
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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We consider the problem of dividing limited resources to individuals arriving over T rounds. Each round has a random number of individuals arrive, and individuals can be characterized by their type (i.e., preferences over the different resources). A standard notion of fairness in this setting is that an allocation simultaneously satisfy envy-freeness and efficiency. The former is an individual guarantee, requiring that each agent prefers the agent’s own allocation over the allocation of any other; in contrast, efficiency is a global property, requiring that the allocations clear the available resources. For divisible resources, when the number of individuals of each type are known up front, the desiderata are simultaneously achievable for a large class of utility functions. However, in an online setting when the number of individuals of each type are only revealed round by round, no policy can guarantee these desiderata simultaneously, and hence, the best one can do is to try and allocate so as to approximately satisfy the two properties. We show that, in the online setting, the two desired properties (envy-freeness and efficiency) are in direct contention in that any algorithm achieving additive counterfactual envy-freeness up to a factor of L T necessarily suffers an efficiency loss of at least [Formula: see text]. We complement this uncertainty principle with a simple algorithm, Guarded-Hope, which allocates resources based on an adaptive threshold policy and is able to achieve any fairness–efficiency point on this frontier. Our results provide guarantees for fair online resource allocation with high probability for multiple resource and multiple type settings. In simulation results, our algorithm provides allocations close to the optimal fair solution in hindsight, motivating its use in practical applications as the algorithm is able to adapt to any desired fairness efficiency trade-off. Funding: This work was supported by the National Science Foundation [Grants ECCS-1847393, DMS-1839346, CCF-1948256, and CNS-1955997] and the Army Research Laboratory [Grant W911NF-17-1-0094]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2022.2397 .more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1145/3606376.3593558
