AI 中文总结
研究在线性空间上有序数偏好的匹配问题，提出以匹配为预测的机制，保证1一致性和3鲁棒性，解决了Filos-Ratsikas等人的开放问题，能在预测准确时恢复最优匹配，不准确时保留最优无预测失真保证。
AI 中文摘要
我们重新审视了在线性空间上具有序数偏好的匹配问题。在经典设置中，在共享的未知线性度量中有n个代理和n个物品，目标是仅使用代理对物品按距离的排名找到低成本完美匹配。如果一种机制在每个一致的线性度量中总是输出成本在最优值的α倍以内的匹配，则该机制具有失真α。在学习增强设置中，该机制还会得到一个传达有关实例的额外信息的预测。此预测的质量未知，目标是在预测准确时（一致性）优化机制的失真，同时在预测任意不准确时（鲁棒性）保持最坏情况保证。我们提出了一种以匹配作为其预测的机制，并保证1一致性和3鲁棒性。通过在预测完全准确时恢复最优匹配，同时在预测任意不准确时保留最优的无预测失真保证，我们解决了Filos-Ratsikas等人（IJCAI，2025）的一个开放问题。
英文摘要
We revisit the problem of matching on the line with ordinal preferences. In the classic setting, there are $n$ agents and $n$ items in a shared unknown line metric, and the goal is to find a low-cost perfect matching using only the agents' rankings of the items by distance. A mechanism has distortion $α$ if it always outputs a matching whose cost is within a factor of $α$ of the optimum, in every consistent line metric. In the learning-augmented setting, the mechanism is also supplied with a prediction that conveys additional information about the instance. The quality of this prediction is unknown, and the goal is to optimize the mechanism's distortion when the prediction is accurate (consistency), while preserving worst-case guarantees when the prediction is arbitrarily inaccurate (robustness). We propose a mechanism that takes a matching as its prediction and guarantees $1$-consistency and $3$-robustness. By recovering an optimal matching when the prediction is perfectly accurate while retaining the optimal prediction-free distortion guarantee when it is arbitrarily inaccurate, we resolve an open question of Filos-Ratsikas et al. (IJCAI, 2025).
