A One-Inclusion Graph Approach to Multi-Group Learning

TL;DR

This paper introduces a new algorithm for multi-group learning based on a one-inclusion graph approach, achieving optimal sample complexity bounds and extending existing strategies with bipartite b-matching.

Contribution

It extends the one-inclusion graph prediction strategy to multi-group learning and establishes tight bounds on sample complexity, including optimal convergence rates.

Findings

Achieves the tightest-known upper bounds on sample complexity.

Provides a lower bound confirming the optimality of the convergence rate.

Achieves the optimal 1/n convergence rate under certain relaxed conditions.

Abstract

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 $\log n / n$ 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.