We prove the tightest-known upper bounds on the sample complexity of multi-group learning. Our algorithm extends the one-inclusion graph prediction strategy using a generalization of bipartite b-matching. In the group-realizable setting, we provide a lower bound confirming that our algorithm's logn/n convergence rate is optimal in general. If one relaxes the learning objective such that the group on which we are evaluated is chosen obliviously of the sample, then our algorithm achieves the optimal 1/n convergence rate under group-realizability.
@article{arxiv.2603.23208,
title = {A One-Inclusion Graph Approach to Multi-Group Learning},
author = {Noah Bergam and Samuel Deng and Daniel Hsu},
journal= {arXiv preprint arXiv:2603.23208},
year = {2026}
}
Comments
An error in the main proof of our main lemma was found by an anonymous reviewer, particularly in the parameter required to find a feasible matching in our reduction to a "multi-group" bipartite matching problem. We did not find a way to fix the error through current techniques