We introduce a new type of query mechanism for collecting human feedback, called the perceptual adjustment query ( PAQ). Being both informative and cognitively lightweight, the PAQ adopts an inverted measurement scheme, and combines advantages from both cardinal and ordinal queries. We showcase the PAQ in the metric learning problem, where we collect PAQ measurements to learn an unknown Mahalanobis distance. This gives rise to a high-dimensional, low-rank matrix estimation problem to which standard matrix estimators cannot be applied. Consequently, we develop a two-stage estimator for metric learning from PAQs, and provide sample complexity guarantees for this estimator. We present numerical simulations demonstrating the performance of the estimator and its notable properties.

翻译：我们提出了一种名为感知调整查询（PAQ）的新型人类反馈收集机制。PAQ采用反向测量方案，兼具信息丰富性和认知轻量级特征，融合了基数查询与序数查询的优势。我们以度量学习问题作为PAQ的应用场景，通过收集PAQ测量值来学习未知的马氏距离。这引出一个标准矩阵估计器无法适用的高维低秩矩阵估计问题。因此，我们开发了基于PAQ的度量学习两阶段估计器，并给出该估计器的样本复杂度保证。最后通过数值模拟实验展示了该估计器的性能及其显著特性。