We study learnability of linear utility functions from pairwise comparison queries. In particular, we consider two learning objectives. The first objective is to predict out-of-sample responses to pairwise comparisons, whereas the second is to approximately recover the true parameters of the utility function. We show that in the passive learning setting, linear utilities are efficiently learnable with respect to the first objective, both when query responses are uncorrupted by noise, and under Tsybakov noise when the distributions are sufficiently "nice". In contrast, we show that utility parameters are not learnable for a large set of data distributions without strong modeling assumptions, even when query responses are noise-free. Next, we proceed to analyze the learning problem in an active learning setting. In this case, we show that even the second objective is efficiently learnable, and present algorithms for both the noise-free and noisy query response settings. Our results thus exhibit a qualitative learnability gap between passive and active learning from pairwise preference queries, demonstrating the value of the ability to select pairwise queries for utility learning.

翻译：研究从成对比较查询中学习线性效用函数的可学习性。具体考虑两个学习目标：第一个目标是预测样本外成对比较的响应，第二个目标则是近似恢复效用函数的真实参数。结果表明，在被动学习框架下，无论查询响应是否受到噪声污染，只要在分布满足足够"优良"的Tsybakov噪声条件下，线性效用函数对第一个目标而言都是高效可学习的。相比之下，当数据分布范围广泛且缺乏强模型假设时，即使查询响应完全无噪声，效用参数也是不可学习的。随后，我们转向主动学习环境中的学习问题分析。在此情形下，我们证明即使是第二个目标也能被高效学习，并针对无噪声和有噪声查询响应两种场景分别提出算法。研究结果清晰揭示了基于成对偏好查询的被动学习与主动学习之间存在本质性的可学习性差异，从而论证了在效用学习中选择成对查询的能力所具有的价值。