Deep Submodular Peripteral Networks

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 contrastive-learning inspired GPC-ready 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, 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 showing superiority in downstream tasks such as experimental design and streaming applications.