Open Problem: Learning with Variational Objectives on Measures
This is an incremental theoretical proposal that could impact researchers in machine learning by suggesting new directions for generalization and weakly-supervised tasks.
The paper identifies a gap in statistical learning theory, which traditionally uses variational objectives on functions, and proposes extending these objectives to measures to address out-of-distribution generalization and weakly-supervised learning, raising open questions about theoretical extensions and practical algorithms.
The theory of statistical learning has focused on variational objectives expressed on functions. In this note, we discuss motivations to write similar objectives on measures, in particular to discuss out-of-distribution generalization and weakly-supervised learning. It raises a natural question: can one cast usual statistical learning results to objectives expressed on measures? Does the resulting construction lead to new algorithms of practical interest?