We consider the task of assigning indivisible goods to a set of agents in a fair manner. Our notion of fairness is Nash social welfare, i.e., the goal is to maximize the geometric mean of the utilities of the agents. Each good comes in multiple items or copies, and the utility of an agent diminishes as it receives more items of the same good. The utility of a bundle of items for an agent is the sum of the utilities of the items in the bundle. Each agent has a utility cap beyond which he does not value additional items. We give a polynomial time approximation algorithm that maximizes Nash social welfare up to a factor of e^{1/{e}} ~ 1.445. The computed allocation is Pareto-optimal and approximates envy-freeness up to one item up to a factor of 2 + epsilon.
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Near-Neighbor Methods in Random Preference Completion
This paper studies a stylized, yet natural, learning-to-rank problem and points out the critical incorrectness of a widely used nearest neighbor algorithm. We consider a model with n agents (users) {xi}i∈[n] and m alternatives (items) {yl}l∈[m], each of which is associated with a latent feature vector. Agents rank items nondeterministically according to the Plackett-Luce model, where the higher the utility of an item to the agent, the more likely this item will be ranked high by the agent. Our goal is to identify near neighbors of an arbitrary agent in the latent space for prediction.
We first show that the Kendall-tau distance based kNN produces incorrect results in our model. Next, we propose a new anchor-based algorithm to find neighbors of an agent. A salient feature of our algorithm is that it leverages the rankings of many other agents (the so-called “anchors”) to determine the closeness/similarities of two agents. We provide a rigorous analysis for one-dimensional latent space, and complement the theoretical results with experiments on synthetic and real datasets. The experiments confirm that the new algorithm is robust and practical.
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- Award ID(s):
- 1755769
- PAR ID:
- 10108717
- Date Published:
- Journal Name:
- Proceedings of the ... AAAI Conference on Artificial Intelligence
- ISSN:
- 2159-5399
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/https://doi.org/10.1609/aaai.v33i01.33014336
