Learning Structured Set Utility Functions with Contrastive Element Representations

TMLR Paper7133 Authors

Abstract: Learning utility functions over sets of elements is central to many machine learning and decision-making tasks such as feature selection, sensor placement, and content recommendation, where the goal is to evaluate and select an optimal subset of elements that provide the largest utility. These utility functions often exhibit desirable properties like monotonicity and submodularity over sets, but are typically expensive to evaluate and may lack an explicit analytical form. Moreover, the utility of a set can vary depending on certain contextual variables, further complicating the learning task. In this work, we propose a unified framework for modeling and learning contextual set functions with monotone submodular structure from data using deep networks equipped with structural regularization. Our key insight is to decompose the set function into two learnable components: (i) a context-conditioned contrastive embedding network that maps elements to a shared latent space based on performance and contextual similarity, and (ii) an aggregation network that predicts set-level utility from the sum of embeddings with a submodular norm-based regularization term encouraging the learned function to exhibit diminishing returns. This combination improves utility prediction for unseen sets and contexts and enables greedy subset selection, which admits near-optimality guarantees. We evaluate our framework on a wide variety of real-world contextual subset selection tasks such as content recommendation, document summarization, and sensor selection demonstrating consistent improvements in utility prediction compared to baselines and stronger subset selection performance under context shifts.

Submission Type: Regular submission (no more than 12 pages of main content)

Assigned Action Editor: ~Sebastian_Tschiatschek1

Submission Number: 7133