Deep Submodular Peripteral Networks

Gantavya Bhatt, Arnav Mohanty Das, Jeff Bilmes

Keywords: Submodular Optimization, Learning Set Functions, Experimental Design, Streaming Summarization, Data subset selection, Knowledge Distillation

TL;DR: This work proposes a new expressive parametric family of submodular functions and new graded-pairwise comparison (GPC) loss functions for their learning from expensive teachers.

Abstract: 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.

Primary Area: Active learning

Submission Number: 14619