Group-realizable multi-group learning by minimizing empirical risk

TL;DR

This paper investigates multi-group learning, demonstrating improved sample complexity in the group-realizable setting and proposing an improper learning approach as a computationally feasible alternative.

Contribution

It introduces the concept of group-realizable multi-group learning, showing theoretical sample complexity improvements and proposing an improper learning method for practical implementation.

Findings

Sample complexity improves in group-realizable setting

Empirical risk minimization over group-realizable concepts is effective

Improper learning offers a computationally feasible alternative

Abstract

The sample complexity of multi-group learning is shown to improve in the group-realizable setting over the agnostic setting, even when the family of groups is infinite so long as it has finite VC dimension. The improved sample complexity is obtained by empirical risk minimization over the class of group-realizable concepts, which itself could have infinite VC dimension. Implementing this approach is also shown to be computationally intractable, and an alternative approach is suggested based on improper learning.