Submodular functions, crucial for various applications, often lack practical learning methods for their acquisition. Seemingly unrelated, learning a scaling from oracles offering graded pairwise preferences (GPC) is underexplored, despite a rich history in psychometrics. In this paper, we introduce deep submodular peripteral networks (DSPNs), a novel parametric family of submodular functions, and methods for their training using a GPC-based strategy to connect and then tackle both of the above challenges. We introduce newly devised GPC-style ``peripteral'' loss which leverages numerically graded relationships between pairs of objects (sets in our case). Unlike traditional contrastive learning, or RHLF preference ranking, our method utilizes graded comparisons, extracting more nuanced information than just binary-outcome comparisons, and contrasts sets of any size (not just two). We also define a novel suite of automatic sampling strategies for training, including active-learning inspired submodular feedback. We demonstrate DSPNs' efficacy in learning submodularity from a costly target submodular function and demonstrate its superiority both for experimental design and online streaming applications.

翻译：子模函数在众多应用中至关重要，但通常缺乏实用的学习方法以获取它们。看似无关的是，尽管在心理测量学中已有悠久历史，但从提供分级成对偏好（GPC）的预言机中学习缩放比例的研究仍显不足。本文中，我们引入了深度子模外周网络（DSPNs），这是一个新颖的子模函数参数族，以及使用基于GPC的训练策略来连接并进而解决上述两个挑战的方法。我们引入了新设计的GPC风格“外周”损失，该损失利用了对象对（在我们的案例中为集合）之间的数值分级关系。与传统的对比学习或RHLF偏好排序不同，我们的方法利用分级比较，提取比仅二元结果比较更细致的信息，并且可以对比任意大小的集合（不仅仅是两个）。我们还定义了一套新颖的自动采样策略用于训练，包括受主动学习启发的子模反馈。我们证明了DSPNs在从代价高昂的目标子模函数中学习子模性的有效性，并展示了其在实验设计和在线流应用中的优越性。