Efficient agnostic learning for group classes

Classify the group classes that admit computationally efficient agnostic learners.

Background

The paper provides a polynomial-time agnostic ERM algorithm for permutations through assignment, but does not determine the computational status of agnostic learning for other group classes. The question concerns the broader algorithmic landscape beyond the specific GL(d,2) hardness problem.

A complete answer would identify structural conditions on a group action that permit efficient optimization or learning in the agnostic model.